**Paul Adrien Maurice Dirac**, OM, FRS (dɪˈræk ; 1902–84) was an

EnglishThe United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...

theoretical physicist who made fundamental contributions to the early development of both

quantum mechanicsQuantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

and

quantum electrodynamicsQuantum electrodynamics is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved...

. He held the Lucasian Chair of Mathematics at the

University of CambridgeThe University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...

and spent the last fourteen years of his life at

Florida State UniversityThe Florida State University is a space-grant and sea-grant public university located in Tallahassee, Florida, United States. It is a comprehensive doctoral research university with medical programs and significant research activity as determined by the Carnegie Foundation...

.

Among other discoveries, he formulated the

Dirac equationThe Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928. It provided a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity, and...

, which describes the behaviour of

fermionIn particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....

s, and predicted the existence of

antimatterIn particle physics, antimatter is the extension of the concept of the antiparticle to matter, where antimatter is composed of antiparticles in the same way that normal matter is composed of particles...

.

Dirac shared the

Nobel Prize in physicsThe Nobel Prize in Physics is awarded once a year by the Royal Swedish Academy of Sciences. It is one of the five Nobel Prizes established by the will of Alfred Nobel in 1895 and awarded since 1901; the others are the Nobel Prize in Chemistry, Nobel Prize in Literature, Nobel Peace Prize, and...

for 1933 with

Erwin SchrödingerErwin Rudolf Josef Alexander Schrödinger was an Austrian physicist and theoretical biologist who was one of the fathers of quantum mechanics, and is famed for a number of important contributions to physics, especially the Schrödinger equation, for which he received the Nobel Prize in Physics in 1933...

, "for the discovery of new productive forms of

atomThe atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...

ic theory."

## Early years

Paul Adrien Maurice Dirac was born at his parents' home in

BristolBristol is a city, unitary authority area and ceremonial county in South West England, with an estimated population of 433,100 for the unitary authority in 2009, and a surrounding Larger Urban Zone with an estimated 1,070,000 residents in 2007...

, England on 8 August 1902, and grew up in the

BishopstonBishopston the name of both a council ward of the city of Bristol, England, and a suburb of the city that falls within that ward. Bishopston is situated around the Gloucester Road , the main northern arterial road in the city. The ward includes St Bonaventures and Ashley Down parishes, as well as...

area of the city. His father, Charles Adrien Ladislas Dirac, was an immigrant from Saint-Maurice in the Canton of

ValaisThe Valais is one of the 26 cantons of Switzerland in the southwestern part of the country, around the valley of the Rhône from its headwaters to Lake Geneva, separating the Pennine Alps from the Bernese Alps. The canton is one of the drier parts of Switzerland in its central Rhône valley...

, Switzerland, who worked in Bristol as a

FrenchThe French are a nation that share a common French culture and speak the French language as a mother tongue. Historically, the French population are descended from peoples of Celtic, Latin and Germanic origin, and are today a mixture of several ethnic groups...

teacher. His mother, Florence Hannah Dirac, née Holten, the daughter of a ship's captain, worked as a librarian at the

Bristol Central LibraryBristol Central Library is a historic building on the south side of College Green, Bristol, England. It contains the main collections of Bristol's public library....

. Paul had a younger sister, Béatrice Isabelle Marguerite, known as Betty, and an older brother, Reginald Charles Félix, known as Felix, who committed suicide in March 1925. Dirac later recalled: "My parents were terribly distressed. I didn't know they cared so much. ...I never knew that parents were supposed to care for their children, but from then on I knew."

Charles and the children were officially Swiss nationals until they became naturalised on 22 October 1919. Dirac's father was strict and authoritarian, although he disapproved of corporal punishment. Dirac had a strained relationship with his father, so much so that after his death, he wrote, "I feel much freer now, and I am my own man." Charles forced his children to speak to him only in French, in order that they learn the language. When Dirac found that he could not express what he wanted to say in French, he chose to remain silent.

Dirac was educated first at

Bishop Road Primary SchoolBishop Road Primary School is the largest primary school in Bristol, notable for having educated Cary Grant, Paul Dirac, John Polkinghorne and Ben J. Green....

and then at the all-boys

Merchant Venturers'The Society of Merchant Venturers is a private entrepreneurial and charitable organisation in the English city of Bristol, which dates back to the 13th century...

Technical College (later

Cotham SchoolCotham School is a secondary school with academy status in Cotham, a suburb of Bristol, England.-History:Its predecessor was the Merchant Venturers School.Until the academic year 2000/01, Cotham was a Grammar School...

), where his father was a French teacher. The school was an institution attached to the

University of BristolThe University of Bristol is a public research university located in Bristol, United Kingdom. One of the so-called "red brick" universities, it received its Royal Charter in 1909, although its predecessor institution, University College, Bristol, had been in existence since 1876.The University is...

, which shared grounds and staff. It emphasised technical subjects like bricklaying, shoemaking and metal work, and modern languages. This was an unusual arrangement at a time when secondary education in Britain was still dedicated largely to the classics, and something for which Dirac would later express gratitude.

Dirac studied

electrical engineeringElectrical engineering is a field of engineering that generally deals with the study and application of electricity, electronics and electromagnetism. The field first became an identifiable occupation in the late nineteenth century after commercialization of the electric telegraph and electrical...

on a City of Bristol University Scholarship at the

University of BristolThe University of Bristol is a public research university located in Bristol, United Kingdom. One of the so-called "red brick" universities, it received its Royal Charter in 1909, although its predecessor institution, University College, Bristol, had been in existence since 1876.The University is...

's engineering faculty, which was co-located with the Merchant Venturers' Technical College. Shortly before he completed his degree in 1921, he sat the entrance examination for

St John's College, CambridgeSt John's College is a constituent college of the University of Cambridge. The college's alumni include nine Nobel Prize winners, six Prime Ministers, three archbishops, at least two princes, and three Saints....

. He passed, and was awarded a £70 scholarship, but this fell short of the amount of money required to live and study at Cambridge. Despite graduating with a first class honours

bachelor of scienceA Bachelor of Science is an undergraduate academic degree awarded for completed courses that generally last three to five years .-Australia:In Australia, the BSc is a 3 year degree, offered from 1st year on...

degree in engineering, the economic climate of the

post-war depression was such that he was unable to find work as an engineer. Instead he took up an offer to study for

bachelor of artsA Bachelor of Arts , from the Latin artium baccalaureus, is a bachelor's degree awarded for an undergraduate course or program in either the liberal arts, the sciences, or both...

degree in mathematics at the University of Bristol free of charge. He was permitted to skip the first year of the course owing to his engineering degree.

In 1923, Dirac graduated, once again with first class honours, and received a £140 scholarship from the

Department of Scientific and Industrial ResearchSeveral countries have organizations called the Department of Scientific and Industrial Research, abbreviated DSIR.-United Kingdom:...

. Along with his £70 scholarship from St John's College, this was enough to live at Cambridge. There, Dirac pursued his interests in the theory of

general relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

, an interest he gained earlier as a student in Bristol, and in the nascent field of quantum physics, under the supervision of Ralph Fowler.

## Career

Dirac noticed an analogy between the

Poisson bracketIn mathematics and classical mechanics, the Poisson bracket is an important binary operation in Hamiltonian mechanics, playing a central role in Hamilton's equations of motion, which govern the time-evolution of a Hamiltonian dynamical system...

s of

classical mechanicsIn physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...

and the recently proposed quantization rules in

Werner HeisenbergWerner Karl Heisenberg was a German theoretical physicist who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory...

's

matrix formulationMatrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925.Matrix mechanics was the first conceptually autonomous and logically consistent formulation of quantum mechanics. It extended the Bohr Model by describing how the quantum jumps...

of quantum mechanics. This observation allowed Dirac to obtain the

quantizationIn physics, quantization is the process of explaining a classical understanding of physical phenomena in terms of a newer understanding known as "quantum mechanics". It is a procedure for constructing a quantum field theory starting from a classical field theory. This is a generalization of the...

rules in a

novel and more illuminating mannerIn physics, canonical quantization is a procedure for quantizing a classical theory while attempting to preserve the formal structure of the classical theory, to the extent possible. Historically, this was Werner Heisenberg's route to obtaining quantum mechanics...

. For this work, published in 1926, he received a Ph.D. from Cambridge.

In 1928, building on 2x2 spin matrices which he discovered independently (

Abraham PaisAbraham Pais was a Dutch-born American physicist and science historian. Pais earned his Ph.D. from University of Utrecht just prior to a Nazi ban on Jewish participation in Dutch universities during World War II...

quoted Dirac as saying "I believe I got these (matrices) independently of Pauli and possibly Pauli got these independently of me") of Wolfgang Pauli's work on non-relativistic

spinIn quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...

systems, he proposed the

Dirac equationThe Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928. It provided a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity, and...

as a

relativisticSpecial relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

equation of motionEquations of motion are equations that describe the behavior of a system in terms of its motion as a function of time...

for the

wavefunctionNot to be confused with the related concept of the Wave equationA wave function or wavefunction is a probability amplitude in quantum mechanics describing the quantum state of a particle and how it behaves. Typically, its values are complex numbers and, for a single particle, it is a function of...

of the

electronThe electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

. This work led Dirac to predict the existence of the

positronThe positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1e, a spin of ½, and has the same mass as an electron...

, the electron's

antiparticleCorresponding to most kinds of particles, there is an associated antiparticle with the same mass and opposite electric charge. For example, the antiparticle of the electron is the positively charged antielectron, or positron, which is produced naturally in certain types of radioactive decay.The...

, which he interpreted in terms of what came to be called the

*Dirac sea*The Dirac sea is a theoretical model of the vacuum as an infinite sea of particles with negative energy. It was first postulated by the British physicist Paul Dirac in 1930 to explain the anomalous negative-energy quantum states predicted by the Dirac equation for relativistic electrons...

. The positron was observed by

Carl AndersonCarl David Anderson was an American physicist. He is best known for his discovery of the positron in 1932, an achievement for which he received the 1936 Nobel Prize in Physics, and of the muon in 1936.-Biography:...

in 1932. Dirac's equation also contributed to explaining the origin of

quantum spinIn quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...

as a relativistic phenomenon.

The necessity of

fermionIn particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....

s (matter being created and destroyed in

Enrico FermiEnrico Fermi was an Italian-born, naturalized American physicist particularly known for his work on the development of the first nuclear reactor, Chicago Pile-1, and for his contributions to the development of quantum theory, nuclear and particle physics, and statistical mechanics...

's 1934 theory of

beta decayIn nuclear physics, beta decay is a type of radioactive decay in which a beta particle is emitted from an atom. There are two types of beta decay: beta minus and beta plus. In the case of beta decay that produces an electron emission, it is referred to as beta minus , while in the case of a...

), however, led to a reinterpretation of Dirac's equation as a "classical"

field equationA field equation is an equation in a physical theory that describes how a fundamental force interacts with matter...

for any

point particleA point particle is an idealization of particles heavily used in physics. Its defining feature is that it lacks spatial extension: being zero-dimensional, it does not take up space...

of spin

*ħ*The Planck constant , also called Planck's constant, is a physical constant reflecting the sizes of energy quanta in quantum mechanics. It is named after Max Planck, one of the founders of quantum theory, who discovered it in 1899...

/2, itself subject to quantization conditions involving

anti-commutatorIn mathematics, anticommutativity is the property of an operation that swapping the position of any two arguments negates the result. Anticommutative operations are widely used in algebra, geometry, mathematical analysis and, as a consequence, in physics: they are often called antisymmetric...

s. Thus reinterpreted, in 1934 by

Werner HeisenbergWerner Karl Heisenberg was a German theoretical physicist who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory...

, as a (quantum) field equation accurately describing all elementary matter particles- today quarks and leptons – this Dirac field equation is as central to theoretical physics as the Maxwell, Yang-Mills and

EinsteinGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

field equations. Dirac is regarded as the founder of

quantum electrodynamicsQuantum electrodynamics is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved...

, being the first to use that term. He also introduced the idea of

vacuum polarizationIn quantum field theory, and specifically quantum electrodynamics, vacuum polarization describes a process in which a background electromagnetic field produces virtual electron–positron pairs that change the distribution of charges and currents that generated the original electromagnetic...

in the early 1930s. This work was key to the development of quantum mechanics by the next generation of theorists, and in particular

SchwingerJulian Seymour Schwinger was an American theoretical physicist. He is best known for his work on the theory of quantum electrodynamics, in particular for developing a relativistically invariant perturbation theory, and for renormalizing QED to one loop order.Schwinger is recognized as one of the...

,

FeynmanRichard Phillips Feynman was an American physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics...

,

Sin-Itiro Tomonagawas a Japanese physicist, influential in the development of quantum electrodynamics, work for which he was jointly awarded the Nobel Prize in Physics in 1965 along with Richard Feynman and Julian Schwinger.-Biography:...

and

DysonFreeman John Dyson FRS is a British-born American theoretical physicist and mathematician, famous for his work in quantum field theory, solid-state physics, astronomy and nuclear engineering. Dyson is a member of the Board of Sponsors of the Bulletin of the Atomic Scientists...

in their formulation of quantum electrodynamics.

Dirac's

*Principles of Quantum Mechanics*The Principles of Quantum Mechanics is a book that describes quantum mechanics, written by Paul Dirac and published in 1930.In this book Dirac gives an account of quantum mechanics by "demonstrating how to construct a completely new theoretical framework from scratch ... [and] .....

, published in 1930, is a landmark in the

history of scienceThe history of science is the study of the historical development of human understandings of the natural world and the domains of the social sciences....

. It quickly became one of the standard textbooks on the subject and is still used today. In that book, Dirac incorporated the previous work of

Werner HeisenbergWerner Karl Heisenberg was a German theoretical physicist who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory...

on

matrix mechanicsMatrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925.Matrix mechanics was the first conceptually autonomous and logically consistent formulation of quantum mechanics. It extended the Bohr Model by describing how the quantum jumps...

and of

Erwin SchrödingerErwin Rudolf Josef Alexander Schrödinger was an Austrian physicist and theoretical biologist who was one of the fathers of quantum mechanics, and is famed for a number of important contributions to physics, especially the Schrödinger equation, for which he received the Nobel Prize in Physics in 1933...

on

wave mechanicsThe Schrödinger equation was formulated in 1926 by Austrian physicist Erwin Schrödinger. Used in physics , it is an equation that describes how the quantum state of a physical system changes in time....

into a single mathematical formalism that associates measurable quantities to operators acting on the

Hilbert spaceThe mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions...

of vectors that describe the state of a

physical systemIn physics, the word system has a technical meaning, namely, it is the portion of the physical universe chosen for analysis. Everything outside the system is known as the environment, which in analysis is ignored except for its effects on the system. The cut between system and the world is a free...

. The book also introduced the

delta functionThe Dirac delta function, or δ function, is a generalized function depending on a real parameter such that it is zero for all values of the parameter except when the parameter is zero, and its integral over the parameter from −∞ to ∞ is equal to one. It was introduced by theoretical...

. Following his 1939 article, he also included the

bra-ket notationBra-ket notation is a standard notation for describing quantum states in the theory of quantum mechanics composed of angle brackets and vertical bars. It can also be used to denote abstract vectors and linear functionals in mathematics...

in the third edition of his book, thereby contributing to its universal use nowadays.

In 1933, following his 1931 paper on magnetic monopoles, Dirac showed that the existence of a single

magnetic monopoleA magnetic monopole is a hypothetical particle in particle physics that is a magnet with only one magnetic pole . In more technical terms, a magnetic monopole would have a net "magnetic charge". Modern interest in the concept stems from particle theories, notably the grand unified and superstring...

in the universe would suffice to explain the observed quantization of electrical charge. In 1975, 1982, and 2009 intriguing results suggested the possible detection of magnetic monopoles, but there is, to date, no direct evidence for their existence.

Dirac was the Lucasian Professor of Mathematics at Cambridge from 1932 to 1969. In 1937, he proposed a speculative

cosmologicalPhysical cosmology, as a branch of astronomy, is the study of the largest-scale structures and dynamics of the universe and is concerned with fundamental questions about its formation and evolution. For most of human history, it was a branch of metaphysics and religion...

model based on the so-called

large numbers hypothesisThe Dirac large numbers hypothesis is an observation made by Paul Dirac in 1937 relating ratios of size scales in the Universe to that of force scales. The ratios constitute very large, dimensionless numbers: some 40 orders of magnitude in the present cosmological epoch...

. During

World War IIWorld War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...

, he conducted important theoretical and experimental research on uranium enrichment by

gas centrifugeA gas centrifuge is a device that performs isotope separation of gases. A centrifuge relies on the principles of centripetal force accelerating molecules so that particles of different masses are physically separated in a gradient along the radius of a rotating container.A prominent use of gas...

.

Dirac's

quantum electrodynamicsQuantum electrodynamics is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved...

made predictions that were – more often than not – infinite and therefore unacceptable. A workaround known as

renormalizationIn quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, renormalization is any of a collection of techniques used to treat infinities arising in calculated quantities....

was developed, but Dirac never accepted this. "I must say that I am very dissatisfied with the situation," he said in 1975, "because this so-called 'good theory' does involve neglecting infinities which appear in its equations, neglecting them in an arbitrary way. This is just not sensible mathematics. Sensible mathematics involves neglecting a quantity when it is small – not neglecting it just because it is infinitely great and you do not want it!" His refusal to accept

renormalizationIn quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, renormalization is any of a collection of techniques used to treat infinities arising in calculated quantities....

, resulted in his work on the subject moving increasingly out of the mainstream. However, from his once rejected notes he managed to work on putting quantum electrodynamics on "logical foundations" based on Hamiltonian formalism that he formulated. He found a rather novel way of deriving the anomalous magnetic moment "Schwinger term" and also the

Lamb shift, afresh, using the Heisenberg picture and without using the joining method used by Weisskopf and French, the two pioneers of modern QED, Schwinger and

FeynmanFeynman may refer to:* Richard Feynman , physicist** Feynman diagram** Feynman graph** Feynman–Kac formula** The Feynman Lectures on Physics** Feynman integral, see Path integral formulation** Feynman parametrization...

, in 1963. That was two years before the Tomonaga-Schwinger-Feynman QED was given formal recognition by an award of the Nobel Prize for physics. Weisskopf and French (FW) were the first to obtain the correct result for the Lamb shift and the anomalous magnetic moment of the electron. At first FW results did not agree with the incorrect but independent results of Feynman and Schwinger (Schweber SS 1994 "QED and the men who made it: Dyson,Feynman,Schwinger and Tomonaga", Princeton :PUP). The 1963–1964 lectures Dirac gave on quantum field theory at Yeshiva University were published in 1966 as the Belfer Graduate School of Science, Monograph Series Number, 3. After having relocated to Florida in order to be near his elder daughter, Mary, Dirac spent his last fourteen years (of both life and physics research) at the

University of MiamiThe University of Miami is a private, non-sectarian university founded in 1925 with its main campus in Coral Gables, Florida, a medical campus in Miami city proper at Civic Center, and an oceanographic research facility on Virginia Key., the university currently enrolls 15,629 students in 12...

in

Coral Gables, FloridaCoral Gables is a city in Miami-Dade County, Florida, southwest of Downtown Miami, in the United States. The city is home to the University of Miami....

and

Florida State UniversityThe Florida State University is a space-grant and sea-grant public university located in Tallahassee, Florida, United States. It is a comprehensive doctoral research university with medical programs and significant research activity as determined by the Carnegie Foundation...

in

Tallahassee, FloridaTallahassee is the capital of the U.S. state of Florida. It is the county seat and only incorporated municipality in Leon County, and is the 128th largest city in the United States. Tallahassee became the capital of Florida, then the Florida Territory, in 1824. In 2010, the population recorded by...

.

In the 1950s in his search for a better QED, Paul Dirac developed the Hamiltonian theory of constraints (Canad J Math 1950 vol 2, 129; 1951 vol 3, 1) based on lectures that he delivered at the 1949 International Mathematical Congress in Canada. Dirac (1951 “The Hamiltonian Form of Field Dynamics” Canad Jour Math, vol 3 ,1) had also solved the problem of putting the Tomonaga-Schwinger equation into the Schrödinger representation (See Phillips R J N 1987 “Tributes to Dirac” p31 London:Adam Hilger) and given explicit expressions for the scalar meson field (spin zero pion or pseudoscalar meson), the vector meson field (spin one rho meson), and the electromagnetic field (spin one massless boson, photon).

The Hamiltonian of constrained systems is one of Dirac’s many masterpieces. It is a powerful generalization of Hamiltonian theory that remains valid for curved spacetime. The equations for the Hamiltonian involve only six degrees of freedom described by

,

for each point of the surface on which the state is considered. The

(m = 0,1,2,3) appear in the theory only through the variables

,

which occur as arbitrary coefficients in the equations of motion. H=∫

x[

–

/

] There are four constraints or weak equations for each point of the surface

= constant. Three of them

form the four vector density in the surface. The fourth

is a 3-dimensional scalar density in the surface

≈0;

≈0 (r=1,2,3)

In the late 1950s he applied the Hamiltonian methods he had developed to cast Einstein’s general relativity in Hamiltonian form (Proc Roy Soc 1958,A vol 246, 333,Phys Rev 1959,vol 114, 924) and to bring to a technical completion the quantization problem of gravitation and bring it also closer to the rest of physics according to Salam and DeWitt. In 1959 also he gave an invited talk on "Energy of the Gravitational Field" at the New York Meeting of the American Physical Society later published in 1959 Phys Rev Lett 2, 368. In 1964 he published his “Lectures on Quantum Mechanics” (London:Academic) which deals with constrained dynamics of nonlinear dynamical systems including quantization of curved spacetime. He also published a paper entitled “Quantization of the Gravitational Field” in 1967 ICTP/IAEA Trieste Symposium on Contemporary Physics.

If one considers waves moving in the direction

resolved into the corresponding Fourier components (r,s = 1,2,3), the variables in the degrees of freedom 13,23,33 are affected by the changes in the coordinate system whereas those in the degrees of freedom 12, (11-22) remain invariant under such changes. The expression for the energy splits up into terms each associated with one of these six degrees of freedom without any cross terms associated with two of them. The degrees of freedom 13, 23, 33 do not appear at all in the expression for energy of gravitational waves in the direction

. The two degrees of freedom 12, (11-22) contribute a positive definite amount of such a form to represent the energy of gravitational waves. These two degrees of freedom correspond in the language of quantum theory , to the gravitational photons (gravitons) with spin +2 or -2 in their direction of motion. The degrees of freedom (11+22) gives rise to the Newtonian potential energy term showing the gravitational force between the two positive mass is attractive and the self energy of every mass is negative.

Amongst his many students was

John PolkinghorneJohn Charlton Polkinghorne KBE FRS is an English theoretical physicist, theologian, writer, and Anglican priest. He was professor of Mathematical physics at the University of Cambridge from 1968 to 1979, when he resigned his chair to study for the priesthood, becoming an ordained Anglican priest...

, who recalls that Dirac "was once asked what was his fundamental belief. He strode to a blackboard and wrote that the laws of nature should be expressed in beautiful equations."

### Family

Dirac married Eugene Wigner's sister, Margit, in 1937. He adopted Margit's two children, Judith and

GabrielGabriel Andrew Dirac was a mathematician who mainly worked in graph theory. He stated a sufficient condition for a graph to contain a Hamiltonian circuit.Dirac received his Ph.D...

. Paul and Margit Dirac had two children together, both daughters, Mary Elizabeth and Florence Monica.

Margit, known as Manci, visited her brother in 1934 in

Princeton-Princeton, New Jersey:*Borough of Princeton, New Jersey*Princeton Township, New Jersey*Princeton, New Jersey -Other places in New Jersey:*Princeton Junction, New Jersey*Princeton Meadows, New Jersey...

from her native Hungary and, while at dinner at the Annex Restaurant (1930s–2006), met the "lonely-looking man at the next table." This account came from a physicist from Korea who met and was influenced by Dirac, Y.S. Kim, who has also written: "It is quite fortunate for the physics community that Manci took good care of our respected Paul A.M. Dirac. Dirac published eleven papers during the period 1939–46.... Dirac was able to maintain his normal research productivity only because Manci was in charge of everything else."

A reviewer of the 2009 biography writes: "Dirac blamed his [emotional] frailties on his father, a Swiss immigrant who bullied his wife, chivvied his children and insisted Paul spoke only French at home, even though the Diracs lived in Bristol. 'I never knew love or affection when I was a child,' Dirac once said." She also writes that "[t]he problem lay with his genes. Both father and son had autism, to differing degrees. Hence the Nobel winner's reticence, literal-mindedness, rigid patterns of behaviour and self-centredness. [Quoting the biography:] 'Dirac's traits as a person with autism were crucial to his success as a theoretical physicist: his ability to order information about mathematics and physics in a systematic way, his visual imagination, his self-centredness, his concentration and determination.'"

### Personality

Dirac was known among his colleagues for his precise and taciturn nature. His colleagues in Cambridge jokingly defined a unit of a dirac which was one word per hour. When

Niels BohrNiels Henrik David Bohr was a Danish physicist who made foundational contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in Physics in 1922. Bohr mentored and collaborated with many of the top physicists of the century at his institute in...

complained that he did not know how to finish a sentence in a scientific article he was writing, Dirac replied, "I was taught at school never to start a sentence without knowing the end of it." He criticized the physicist J. Robert Oppenheimer's interest in poetry: "The aim of science is to make difficult things understandable in a simpler way; the aim of poetry is to state simple things in an incomprehensible way. The two are incompatible."

Dirac himself wrote in his diary during his postgraduate years that he concentrated solely on his research, and only stopped on Sunday, when he took long strolls alone.

An anecdote recounted in a review of the 2009 biography tells of

Werner HeisenbergWerner Karl Heisenberg was a German theoretical physicist who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory...

and Dirac sailing on a cruise ship to a conference in Japan in August 1929. "Both still in their twenties, and unmarried, they made an odd couple. Heisenberg was a ladies' man who constantly flirted and danced, while Dirac—'an Edwardian geek', as [biographer] Graham Farmelo puts it—suffered agonies if forced into any kind of socialising or small talk. 'Why do you dance?' Dirac asked his companion. 'When there are nice girls, it is a pleasure,' Heisenberg replied. Dirac pondered this notion, then blurted out: 'But, Heisenberg, how do you know beforehand that the girls are nice?'"

According to a story told in different versions, a friend or student visited Dirac, not knowing of his marriage. Noticing the visitor's surprise at seeing an attractive woman in the house, Dirac said, "This is... this is Wigner's sister". Margit Dirac told both

George GamowGeorge Gamow , born Georgiy Antonovich Gamov , was a Russian-born theoretical physicist and cosmologist. He discovered alpha decay via quantum tunneling and worked on radioactive decay of the atomic nucleus, star formation, stellar nucleosynthesis, Big Bang nucleosynthesis, cosmic microwave...

and Anton Capri in the 1960s that her husband had actually said, "Allow me to present Wigner's sister, who is now my wife."

Another story told of Dirac is that when he first met the young Richard Feynman at a conference, he said after a long silence "I have an equation. Do you have one too?".

Dirac was also noted for his personal modesty. He called the equation for the

time evolutionTime evolution is the change of state brought about by the passage of time, applicable to systems with internal state . In this formulation, time is not required to be a continuous parameter, but may be discrete or even finite. In classical physics, time evolution of a collection of rigid bodies...

of a quantum-mechanical operator, which he was the first to write down, the "Heisenberg equation of motion". Most physicists speak of

Fermi-Dirac statisticsFermi–Dirac statistics is a part of the science of physics that describes the energies of single particles in a system comprising many identical particles that obey the Pauli Exclusion Principle...

for half-integer-spin particles and Bose-Einstein statistics for integer-spin particles. While lecturing later in life, Dirac always insisted on calling the former "Fermi statistics". He referred to the latter as "Einstein statistics" for reasons, he explained, of "symmetry".

### Religious views

Heisenberg recollected a conversation among young participants at the 1927

Solvay ConferenceThe International Solvay Institutes for Physics and Chemistry, located in Brussels, were founded by the Belgian industrialist Ernest Solvay in 1912, following the historic invitation-only 1911 Conseil Solvay, the turning point in world physics...

about Einstein and

PlanckMax Karl Ernst Ludwig Planck, ForMemRS, was a German physicist who actualized the quantum physics, initiating a revolution in natural science and philosophy. He is regarded as the founder of the quantum theory, for which he received the Nobel Prize in Physics in 1918.-Life and career:Planck came...

's views on religion.

Wolfgang PauliWolfgang Ernst Pauli was an Austrian theoretical physicist and one of the pioneers of quantum physics. In 1945, after being nominated by Albert Einstein, he received the Nobel Prize in Physics for his "decisive contribution through his discovery of a new law of Nature, the exclusion principle or...

, Heisenberg and Dirac took part in it. Dirac's contribution was a criticism of the political purpose of religion, which was much appreciated for its lucidity by Bohr when Heisenberg reported it to him later. Among other things, Dirac said:

Heisenberg's view was tolerant. Pauli, raised as a Catholic, had kept silent after some initial remarks, but when finally he was asked for his opinion, said: "Well, our friend Dirac has got a religion and its guiding principle is 'There is no God and Paul Dirac is His prophet.'" Everybody, including Dirac, burst into laughter.

He may have reversed his views of God later, as this quote from May 1963's Scientific American suggests:

"It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it. One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better."

## Death and commemoration

In 1984, Dirac died in Tallahassee, Florida and was buried at Tallahassee's Roselawn Cemetery. Dirac's childhood home in

BristolBristol is a city, unitary authority area and ceremonial county in South West England, with an estimated population of 433,100 for the unitary authority in 2009, and a surrounding Larger Urban Zone with an estimated 1,070,000 residents in 2007...

is commemorated with a

blue plaqueA blue plaque is a permanent sign installed in a public place to commemorate a link between that location and a famous person or event, serving as a historical marker....

and the nearby Dirac Road is named in recognition of his links with the city. A plaque on the wall at the

Bishop Road Primary SchoolBishop Road Primary School is the largest primary school in Bristol, notable for having educated Cary Grant, Paul Dirac, John Polkinghorne and Ben J. Green....

shows the Dirac equation. A commemorative stone was erected in a garden

Saint-MauriceSaint-Maurice, or Saint-Maurice-en-Valais, is a municipality and district capital of the district of Saint-Maurice in the canton of Valais in Switzerland.It is the site of the Roman outpost of Agaunum and the mediaeval St...

, Switzerland, the town of origin of his father's family, on 1 August 1991. On 13 November 1995 a commemorative marker, made from Burlington green

slateSlate is a fine-grained, foliated, homogeneous metamorphic rock derived from an original shale-type sedimentary rock composed of clay or volcanic ash through low-grade regional metamorphism. The result is a foliated rock in which the foliation may not correspond to the original sedimentary layering...

and inscribed with the Dirac equation, was unveiled in

Westminster AbbeyThe Collegiate Church of St Peter at Westminster, popularly known as Westminster Abbey, is a large, mainly Gothic church, in the City of Westminster, London, United Kingdom, located just to the west of the Palace of Westminster. It is the traditional place of coronation and burial site for English,...

. Objections by the Dean of Westminster, Edward Carpenter, that Dirac was an atheist were brushed aside.

Dirac shared the 1933

Nobel PrizeThe Nobel Prizes are annual international awards bestowed by Scandinavian committees in recognition of cultural and scientific advances. The will of the Swedish chemist Alfred Nobel, the inventor of dynamite, established the prizes in 1895...

for physics with

Erwin SchrödingerErwin Rudolf Josef Alexander Schrödinger was an Austrian physicist and theoretical biologist who was one of the fathers of quantum mechanics, and is famed for a number of important contributions to physics, especially the Schrödinger equation, for which he received the Nobel Prize in Physics in 1933...

"for the discovery of new productive forms of atomic theory." Dirac was also awarded the

Royal MedalThe Royal Medal, also known as The Queen's Medal, is a silver-gilt medal awarded each year by the Royal Society, two for "the most important contributions to the advancement of natural knowledge" and one for "distinguished contributions in the applied sciences" made within the Commonwealth of...

in 1939 and both the

Copley MedalThe Copley Medal is an award given by the Royal Society of London for "outstanding achievements in research in any branch of science, and alternates between the physical sciences and the biological sciences"...

and the

Max Planck medalThe Max Planck medal is an award for extraordinary achievements in theoretical physics. It is awarded annually by the Deutsche Physikalische Gesellschaft , the world's largest organization of physicists.-List of recipients:...

in 1952. He was elected a Fellow of the

Royal SocietyThe Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...

in 1930, an Honorary Fellow of the

American Physical SocietyThe American Physical Society is the world's second largest organization of physicists, behind the Deutsche Physikalische Gesellschaft. The Society publishes more than a dozen scientific journals, including the world renowned Physical Review and Physical Review Letters, and organizes more than 20...

in 1948, and an Honorary Fellow of the

Institute of PhysicsThe Institute of Physics is a scientific charity devoted to increasing the practice, understanding and application of physics. It has a worldwide membership of around 40,000....

, London in 1971. Dirac became a member of the

Order of MeritThe Order of Merit is a British dynastic order recognising distinguished service in the armed forces, science, art, literature, or for the promotion of culture...

, an outstanding recognition by the land of his birth, in 1973. He had previously turned down a

knightA knight was a member of a class of lower nobility in the High Middle Ages.By the Late Middle Ages, the rank had become associated with the ideals of chivalry, a code of conduct for the perfect courtly Christian warrior....

hood, as he did not want to be addressed by his first name.

In 1975, Dirac gave a series of five lectures at the

University of New South WalesThe University of New South Wales , is a research-focused university based in Kensington, a suburb in Sydney, New South Wales, Australia...

which were subsequently published as a book,

*Directions of Physics* (1978). He donated the royalties from this book to the university for the establishment of the

Dirac Lecture SeriesThe Dirac Prize is the name of four prominent awards in the field of theoretical physics, computational chemistry, and mathematics, awarded by different organizations, named in honour of Professor Paul Dirac, one of the great theoretical physicists of the 20th Century.- The Dirac Medal and Lecture...

. The Silver Dirac Medal for the Advancement of Theoretical Physics is awarded by the University of New South Wales on the occasion of the lecture.

Immediately after his death, two organisations of professional physicists established annual

awards in Dirac's memoryThe Dirac Prize is the name of four prominent awards in the field of theoretical physics, computational chemistry, and mathematics, awarded by different organizations, named in honour of Professor Paul Dirac, one of the great theoretical physicists of the 20th Century.- The Dirac Medal and Lecture...

. The

Institute of PhysicsThe Institute of Physics is a scientific charity devoted to increasing the practice, understanding and application of physics. It has a worldwide membership of around 40,000....

, the United Kingdom's professional body for physicists, awards the Paul Dirac Medal and Prize for "outstanding contributions to theoretical (including mathematical and computational) physics". The first three recipients were

Stephen HawkingStephen William Hawking, CH, CBE, FRS, FRSA is an English theoretical physicist and cosmologist, whose scientific books and public appearances have made him an academic celebrity...

(1987),

John Stewart BellJohn Stewart Bell FRS was a British physicist from Northern Ireland , and the originator of Bell's theorem, a significant theorem in quantum physics regarding hidden variable theories.- Early life and work :...

(1988), and

Roger PenroseSir Roger Penrose OM FRS is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute, University of Oxford and Emeritus Fellow of Wadham College...

(1989). The

Abdus Salam International Centre for Theoretical PhysicsThe Abdus Salam International Centre for Theoretical Physics was founded in 1964 by Pakistani scientist and Nobel Laureate Abdus Salam after consulting with Munir Ahmad Khan. It operates under a tripartite agreement among the Italian Government, UNESCO, and International Atomic Energy Agency...

(ICTP) awards the Dirac Medal of the ICTP each year on Dirac's birthday (8 August). Also, the

Dirac PrizeThe Dirac Prize is the name of four prominent awards in the field of theoretical physics, computational chemistry, and mathematics, awarded by different organizations, named in honour of Professor Paul Dirac, one of the great theoretical physicists of the 20th Century.- The Dirac Medal and Lecture...

is awarded by the

International Centre for Theoretical PhysicsThe Abdus Salam International Centre for Theoretical Physics was founded in 1964 by Pakistani scientist and Nobel Laureate Abdus Salam after consulting with Munir Ahmad Khan. It operates under a tripartite agreement among the Italian Government, UNESCO, and International Atomic Energy Agency...

in his memory. Dirac House in Bristol is the headquarters of Institute of Physics Publishing.

The Dirac-Hellmann Award at Florida State University was endowed by Dr Bruce P. Hellmann (Dirac's last doctoral student) in 1997 to reward outstanding work in theoretical physics by FSU researchers. The Paul A.M. Dirac Science Library at Florida State University, which Manci opened in December 1989, is named in his honour, and his papers are held there. Outside is a statue of him by Gabriella Bollobás. The street on which the National High Magnetic Field Laboratory in Tallahassee, Florida, is located was named Paul Dirac Drive. As well as in his home town of Bristol, UK, there is also a road named after him in

DidcotDidcot is a town and civil parish in Oxfordshire about south of Oxford. Until 1974 it was in Berkshire, but was transferred to Oxfordshire in that year, and from Wallingford Rural District to the district of South Oxfordshire...

Oxfordshire, Dirac Way. The BBC named its

video codec DiracDirac is an open and royalty-free video compression format, specification and system developed by BBC Research at the BBC. Schrödinger and dirac-research are open and royalty-free software implementations of Dirac...

in his honour.

## Legacy

Dirac is widely regarded as one of the world's greatest physicists. He was one of the founders of

quantum mechanicsQuantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

and

quantum electrodynamicsQuantum electrodynamics is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved...

.

His early contributions include the modern operator calculus for quantum mechanics, which he called transformation theory, and an early version of the

path integralThe path integral formulation of quantum mechanics is a description of quantum theory which generalizes the action principle of classical mechanics...

. He formulated a many-body formalism for quantum mechanics which allowed each particle to have its own

proper timeIn relativity, proper time is the elapsed time between two events as measured by a clock that passes through both events. The proper time depends not only on the events but also on the motion of the clock between the events. An accelerated clock will measure a smaller elapsed time between two...

.

His relativistic

wave equationThe wave equation is an important second-order linear partial differential equation for the description of waves – as they occur in physics – such as sound waves, light waves and water waves. It arises in fields like acoustics, electromagnetics, and fluid dynamics...

for the electron was the first successful attack on the problem of relativistic quantum mechanics. Dirac founded

quantum field theoryQuantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...

with his reinterpretation of the

Dirac equationThe Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928. It provided a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity, and...

as a many-body equation, which predicted the existence of

antimatterIn particle physics, antimatter is the extension of the concept of the antiparticle to matter, where antimatter is composed of antiparticles in the same way that normal matter is composed of particles...

and matter–antimatter annihilation. He was the first to formulate

quantum electrodynamicsQuantum electrodynamics is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved...

, although he could not calculate arbitrary quantities because the short distance limit requires

renormalizationIn quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, renormalization is any of a collection of techniques used to treat infinities arising in calculated quantities....

.

In an attempt to solve the quantum divergence problem, Dirac gave a classical point particle theory combining advanced and retarded waves to eliminate the classical electron

self-energyIn theoretical physics and quantum field theory a particle's self-energy \Sigma represents the contribution to the particle's energy, or effective mass, due to interactions between the particle and the system it is part of...

. Although these classical methods did not immediately solve the problems in quantum electrodynamics, they did lead

John Archibald WheelerJohn Archibald Wheeler was an American theoretical physicist who was largely responsible for reviving interest in general relativity in the United States after World War II. Wheeler also worked with Niels Bohr in explaining the basic principles behind nuclear fission...

and

Richard FeynmanRichard Phillips Feynman was an American physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics...

to formulate an alternative

Green's functionIn many-body theory, the term Green's function is sometimes used interchangeably with correlation function, but refers specifically to correlators of field operators or creation and annihilation operators....

description for light, which eventually led to Feynman's point particle formulation of quantum field theory.

Dirac discovered the

magnetic monopoleA magnetic monopole is a hypothetical particle in particle physics that is a magnet with only one magnetic pole . In more technical terms, a magnetic monopole would have a net "magnetic charge". Modern interest in the concept stems from particle theories, notably the grand unified and superstring...

solutions, the first topological configuration in physics, and used them to give the modern explanation of charge quantization. He developed constrained quantization in the 1960s, identifying the general quantum rules for arbitrary classical systems.

Dirac's quantum-field analysis of the vibrations of a membrane, in the early 1960s, proved extremely useful to modern practitioners of

superstring theorySuperstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modelling them as vibrations of tiny supersymmetric strings...

and its closely related successor,

M-TheoryIn theoretical physics, M-theory is an extension of string theory in which 11 dimensions are identified. Because the dimensionality exceeds that of superstring theories in 10 dimensions, proponents believe that the 11-dimensional theory unites all five string theories...

.

## See also

- Dirac comb
In mathematics, a Dirac comb is a periodic Schwartz distribution constructed from Dirac delta functions...

- Dirac delta function
The Dirac delta function, or δ function, is a generalized function depending on a real parameter such that it is zero for all values of the parameter except when the parameter is zero, and its integral over the parameter from −∞ to ∞ is equal to one. It was introduced by theoretical...

,
- Dirac large numbers hypothesis
The Dirac large numbers hypothesis is an observation made by Paul Dirac in 1937 relating ratios of size scales in the Universe to that of force scales. The ratios constitute very large, dimensionless numbers: some 40 orders of magnitude in the present cosmological epoch...

- Dirac notation
- Dirac matrices
- Dirac Prize
The Dirac Prize is the name of four prominent awards in the field of theoretical physics, computational chemistry, and mathematics, awarded by different organizations, named in honour of Professor Paul Dirac, one of the great theoretical physicists of the 20th Century.- The Dirac Medal and Lecture...

- Negative probability
In 1942, Paul Dirac wrote a paper "The Physical Interpretation of Quantum Mechanics" where he introduced the concept of negative energies and negative probabilities:...

## Dirac videos

## External links

- Dirac Medal of the International Centre for Theoretical Physics
The Abdus Salam International Centre for Theoretical Physics was founded in 1964 by Pakistani scientist and Nobel Laureate Abdus Salam after consulting with Munir Ahmad Khan. It operates under a tripartite agreement among the Italian Government, UNESCO, and International Atomic Energy Agency...

- Dirac Medal of the World Association of Theoretical and Computational Chemists
The World Association of Theoretical and Computational Chemists is a scholarly association founded in 1982 "in order to encourage the development and application of theoretical methods" in chemistry, particularly quantum chemistry and computational chemistry...

(WATOC)
- The Paul Dirac Collection at Florida State University
- The Paul A. M. Dirac Collection Finding Aid at Florida State University
- Photocopies of Dirac's papers from the Florida State University collection, held under Dirac's name in the Archive Centre of Churchill College, Cambridge
Churchill College is a constituent college of the University of Cambridge, England.In 1958, a Trust was established with Sir Winston Churchill as its Chairman of Trustees, to build and endow a college for 60 fellows and 540 Students as a national and Commonwealth memorial to Winston Churchill; its...

, UK
- Letters from Dirac (1932–36) and other papers, held in the Personal Papers archives of St John's College, Cambridge
St John's College is a constituent college of the University of Cambridge. The college's alumni include nine Nobel Prize winners, six Prime Ministers, three archbishops, at least two princes, and three Saints....

, UK
- Free online access to Dirac's classic 1920s papers from Royal Society's Proceedings A
- Annotated bibliography for Paul Dirac from the Alsos Digital Library for Nuclear Issues
- Oral History interview transcript with Paul Dirac 1 April 1962, 6, 7, 10, & 14 May 1963, American Institute of Physics, Niels Bohr Library and Archives
- Photos of Paul Dirac at the Emilio Segrè Visual Archives, American Institute of Physics
- 2010 June 24 – ScienceTalk Part 1 of interview with Graham Farmelo author of The Strangest Man of Science
- 2010 June 24 – ScienceTalk Part 2 of interview with Graham Farmelo author of The Strangest Man of Science