In
particle physicsParticle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...
, the
electroweak interaction is the
unified descriptionIn physics, a unified field theory, occasionally referred to as a uniform field theory, is a type of field theory that allows all that is usually thought of as fundamental forces and elementary particles to be written in terms of a single field. There is no accepted unified field theory, and thus...
of two of the four known
fundamental interactionIn particle physics, fundamental interactions are the ways that elementary particles interact with one another...
s of nature:
electromagnetismElectromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
and the
weak interactionWeak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...
. Although these two forces appear very different at everyday low energies, the theory models them as two different aspects of the same force. Above the
unification energy, on the order of 100
GeVGEV or GeV may stand for:*GeV or gigaelectronvolt, a unit of energy equal to billion electron volts*GEV or Grid Enabled Vehicle that is fully or partially powered by the electric grid, see plug-in electric vehicle...
, they would merge into a single
electroweak force. Thus if the universe is hot enough (approximately 10
15 KThe kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...
, a temperature exceeded until shortly after the
Big BangThe Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...
) then the electromagnetic force and weak force will merge into a combined electroweak force.
For contributions to the unification of the weak and electromagnetic interaction between
elementary particleIn particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...
s,
Abdus SalamMohammad Abdus Salam, NI, SPk Mohammad Abdus Salam, NI, SPk Mohammad Abdus Salam, NI, SPk (Urdu: محمد عبد السلام, pronounced , (January 29, 1926– November 21, 1996) was a Pakistani theoretical physicist and Nobel laureate in Physics for his work on the electroweak unification of the...
,
Sheldon GlashowSheldon Lee Glashow is a Nobel Prize winning American theoretical physicist. He is the Metcalf Professor of Mathematics and Physics at Boston University.-Birth and education:...
and
Steven WeinbergSteven Weinberg is an American theoretical physicist and Nobel laureate in Physics for his contributions with Abdus Salam and Sheldon Glashow to the unification of the weak force and electromagnetic interaction between elementary particles....
were awarded 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...
in 1979. The existence of the electroweak interactions was experimentally established in two stages, the first being the discovery of
neutral currentWeak neutral current interactions are one of the ways in which subatomic particles can interact by means of the weak force. These interactions are mediated by the boson...
s in neutrino scattering by the
GargamelleGargamelle was a giant bubble chamber detector at CERN, designed mainly for the detection of neutrino interactions. Built in France, with a diameter of nearly 2 meters and 4.8 meters in length, Gargamelle held nearly 12 cubic meters of freon...
collaboration in 1973, and the second in 1983 by the
UA1The UA1 experiment was a high-energy physics experiment that ran at CERN's Super Proton Synchrotron accelerator-collider from 1981 until 1993...
and the
UA2The UA2 high energy physics experiment was one of the two major experiments and collaborations at the CERN proton-antiproton collider SPS, and codiscovered the W and Z bosons in 1983, along with UA1.-External links:*****...
collaborations that involved the discovery of the
W and ZThe W and Z bosons are the elementary particles that mediate the weak interaction; their symbols are , and . The W bosons have a positive and negative electric charge of 1 elementary charge respectively and are each other's antiparticle. The Z boson is electrically neutral and its own...
gauge bosonIn particle physics, gauge bosons are bosonic particles that act as carriers of the fundamental forces of nature. More specifically, elementary particles whose interactions are described by gauge theory exert forces on each other by the exchange of gauge bosons, usually as virtual particles.-...
s in proton-antiproton collisions at the converted
Super Proton SynchrotronThe Super Proton Synchrotron is a particle accelerator of the synchrotron type at CERN. It is housed in a circular tunnel, in circumference, straddling the border of France and Switzerland near Geneva, Switzerland. The SPS was designed by a team led by John Adams, director-general of what was...
.
Formulation
Mathematically, the unification is accomplished under an
SU(2) ×
U(1)
gauge groupIn physics, gauge invariance is the property of a field theory in which different configurations of the underlying fundamental but unobservable fields result in identical observable quantities. A theory with such a property is called a gauge theory...
. The corresponding
gauge bosonIn particle physics, gauge bosons are bosonic particles that act as carriers of the fundamental forces of nature. More specifically, elementary particles whose interactions are described by gauge theory exert forces on each other by the exchange of gauge bosons, usually as virtual particles.-...
s are the
three W bosons of
weak isospinIn particle physics, weak isospin is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol T or I with the third component written as Tz, T3, Iz or I3...
from SU(2) , and the B
0 boson of
weak hyperchargeThe weak hypercharge in particle physics is a conserved quantum number relating the electrical charge and the third component of weak isospin, and is similar to the Gell-Mann–Nishijima formula for the hypercharge of strong interactions...
from U(1), respectively, all of which are massless.
In the
Standard ModelThe Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...
, the
{{Standard model of particle physics|cTopic=Some models}}
In particle physicsParticle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...
, the
electroweak interaction is the
unified descriptionIn physics, a unified field theory, occasionally referred to as a uniform field theory, is a type of field theory that allows all that is usually thought of as fundamental forces and elementary particles to be written in terms of a single field. There is no accepted unified field theory, and thus...
of two of the four known
fundamental interactionIn particle physics, fundamental interactions are the ways that elementary particles interact with one another...
s of nature:
electromagnetismElectromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
and the
weak interactionWeak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...
. Although these two forces appear very different at everyday low energies, the theory models them as two different aspects of the same force. Above the
unification energy, on the order of 100
GeVGEV or GeV may stand for:*GeV or gigaelectronvolt, a unit of energy equal to billion electron volts*GEV or Grid Enabled Vehicle that is fully or partially powered by the electric grid, see plug-in electric vehicle...
, they would merge into a single
electroweak force. Thus if the universe is hot enough (approximately 10
15 KThe kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...
, a temperature exceeded until shortly after the
Big BangThe Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...
) then the electromagnetic force and weak force will merge into a combined electroweak force.
For contributions to the unification of the weak and electromagnetic interaction between
elementary particleIn particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...
s,
Abdus SalamMohammad Abdus Salam, NI, SPk Mohammad Abdus Salam, NI, SPk Mohammad Abdus Salam, NI, SPk (Urdu: محمد عبد السلام, pronounced , (January 29, 1926– November 21, 1996) was a Pakistani theoretical physicist and Nobel laureate in Physics for his work on the electroweak unification of the...
,
Sheldon GlashowSheldon Lee Glashow is a Nobel Prize winning American theoretical physicist. He is the Metcalf Professor of Mathematics and Physics at Boston University.-Birth and education:...
and
Steven WeinbergSteven Weinberg is an American theoretical physicist and Nobel laureate in Physics for his contributions with Abdus Salam and Sheldon Glashow to the unification of the weak force and electromagnetic interaction between elementary particles....
were awarded 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...
in 1979. The existence of the electroweak interactions was experimentally established in two stages, the first being the discovery of
neutral currentWeak neutral current interactions are one of the ways in which subatomic particles can interact by means of the weak force. These interactions are mediated by the boson...
s in neutrino scattering by the
GargamelleGargamelle was a giant bubble chamber detector at CERN, designed mainly for the detection of neutrino interactions. Built in France, with a diameter of nearly 2 meters and 4.8 meters in length, Gargamelle held nearly 12 cubic meters of freon...
collaboration in 1973, and the second in 1983 by the
UA1The UA1 experiment was a high-energy physics experiment that ran at CERN's Super Proton Synchrotron accelerator-collider from 1981 until 1993...
and the
UA2The UA2 high energy physics experiment was one of the two major experiments and collaborations at the CERN proton-antiproton collider SPS, and codiscovered the W and Z bosons in 1983, along with UA1.-External links:*****...
collaborations that involved the discovery of the
W and ZThe W and Z bosons are the elementary particles that mediate the weak interaction; their symbols are , and . The W bosons have a positive and negative electric charge of 1 elementary charge respectively and are each other's antiparticle. The Z boson is electrically neutral and its own...
gauge bosonIn particle physics, gauge bosons are bosonic particles that act as carriers of the fundamental forces of nature. More specifically, elementary particles whose interactions are described by gauge theory exert forces on each other by the exchange of gauge bosons, usually as virtual particles.-...
s in proton-antiproton collisions at the converted
Super Proton SynchrotronThe Super Proton Synchrotron is a particle accelerator of the synchrotron type at CERN. It is housed in a circular tunnel, in circumference, straddling the border of France and Switzerland near Geneva, Switzerland. The SPS was designed by a team led by John Adams, director-general of what was...
.
Formulation
Mathematically, the unification is accomplished under an
SU(2) ×
U(1)
gauge groupIn physics, gauge invariance is the property of a field theory in which different configurations of the underlying fundamental but unobservable fields result in identical observable quantities. A theory with such a property is called a gauge theory...
. The corresponding
gauge bosonIn particle physics, gauge bosons are bosonic particles that act as carriers of the fundamental forces of nature. More specifically, elementary particles whose interactions are described by gauge theory exert forces on each other by the exchange of gauge bosons, usually as virtual particles.-...
s are the
three W bosons of
weak isospinIn particle physics, weak isospin is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol T or I with the third component written as Tz, T3, Iz or I3...
from SU(2) ({{SubatomicParticle|W boson+}}, {{SubatomicParticle|W boson0}}, and {{SubatomicParticle|W boson-}}), and the B
0 boson of
weak hyperchargeThe weak hypercharge in particle physics is a conserved quantum number relating the electrical charge and the third component of weak isospin, and is similar to the Gell-Mann–Nishijima formula for the hypercharge of strong interactions...
from U(1), respectively, all of which are massless.
In the
Standard ModelThe Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...
, the
{{Standard model of particle physics|cTopic=Some models}}
In particle physicsParticle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...
, the
electroweak interaction is the
unified descriptionIn physics, a unified field theory, occasionally referred to as a uniform field theory, is a type of field theory that allows all that is usually thought of as fundamental forces and elementary particles to be written in terms of a single field. There is no accepted unified field theory, and thus...
of two of the four known
fundamental interactionIn particle physics, fundamental interactions are the ways that elementary particles interact with one another...
s of nature:
electromagnetismElectromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
and the
weak interactionWeak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...
. Although these two forces appear very different at everyday low energies, the theory models them as two different aspects of the same force. Above the
unification energy, on the order of 100
GeVGEV or GeV may stand for:*GeV or gigaelectronvolt, a unit of energy equal to billion electron volts*GEV or Grid Enabled Vehicle that is fully or partially powered by the electric grid, see plug-in electric vehicle...
, they would merge into a single
electroweak force. Thus if the universe is hot enough (approximately 10
15 KThe kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...
, a temperature exceeded until shortly after the
Big BangThe Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...
) then the electromagnetic force and weak force will merge into a combined electroweak force.
For contributions to the unification of the weak and electromagnetic interaction between
elementary particleIn particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...
s,
Abdus SalamMohammad Abdus Salam, NI, SPk Mohammad Abdus Salam, NI, SPk Mohammad Abdus Salam, NI, SPk (Urdu: محمد عبد السلام, pronounced , (January 29, 1926– November 21, 1996) was a Pakistani theoretical physicist and Nobel laureate in Physics for his work on the electroweak unification of the...
,
Sheldon GlashowSheldon Lee Glashow is a Nobel Prize winning American theoretical physicist. He is the Metcalf Professor of Mathematics and Physics at Boston University.-Birth and education:...
and
Steven WeinbergSteven Weinberg is an American theoretical physicist and Nobel laureate in Physics for his contributions with Abdus Salam and Sheldon Glashow to the unification of the weak force and electromagnetic interaction between elementary particles....
were awarded 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...
in 1979. The existence of the electroweak interactions was experimentally established in two stages, the first being the discovery of
neutral currentWeak neutral current interactions are one of the ways in which subatomic particles can interact by means of the weak force. These interactions are mediated by the boson...
s in neutrino scattering by the
GargamelleGargamelle was a giant bubble chamber detector at CERN, designed mainly for the detection of neutrino interactions. Built in France, with a diameter of nearly 2 meters and 4.8 meters in length, Gargamelle held nearly 12 cubic meters of freon...
collaboration in 1973, and the second in 1983 by the
UA1The UA1 experiment was a high-energy physics experiment that ran at CERN's Super Proton Synchrotron accelerator-collider from 1981 until 1993...
and the
UA2The UA2 high energy physics experiment was one of the two major experiments and collaborations at the CERN proton-antiproton collider SPS, and codiscovered the W and Z bosons in 1983, along with UA1.-External links:*****...
collaborations that involved the discovery of the
W and ZThe W and Z bosons are the elementary particles that mediate the weak interaction; their symbols are , and . The W bosons have a positive and negative electric charge of 1 elementary charge respectively and are each other's antiparticle. The Z boson is electrically neutral and its own...
gauge bosonIn particle physics, gauge bosons are bosonic particles that act as carriers of the fundamental forces of nature. More specifically, elementary particles whose interactions are described by gauge theory exert forces on each other by the exchange of gauge bosons, usually as virtual particles.-...
s in proton-antiproton collisions at the converted
Super Proton SynchrotronThe Super Proton Synchrotron is a particle accelerator of the synchrotron type at CERN. It is housed in a circular tunnel, in circumference, straddling the border of France and Switzerland near Geneva, Switzerland. The SPS was designed by a team led by John Adams, director-general of what was...
.
Formulation
Mathematically, the unification is accomplished under an
SU(2) ×
U(1)
gauge groupIn physics, gauge invariance is the property of a field theory in which different configurations of the underlying fundamental but unobservable fields result in identical observable quantities. A theory with such a property is called a gauge theory...
. The corresponding
gauge bosonIn particle physics, gauge bosons are bosonic particles that act as carriers of the fundamental forces of nature. More specifically, elementary particles whose interactions are described by gauge theory exert forces on each other by the exchange of gauge bosons, usually as virtual particles.-...
s are the
three W bosons of
weak isospinIn particle physics, weak isospin is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol T or I with the third component written as Tz, T3, Iz or I3...
from SU(2) ({{SubatomicParticle|W boson+}}, {{SubatomicParticle|W boson0}}, and {{SubatomicParticle|W boson-}}), and the B
0 boson of
weak hyperchargeThe weak hypercharge in particle physics is a conserved quantum number relating the electrical charge and the third component of weak isospin, and is similar to the Gell-Mann–Nishijima formula for the hypercharge of strong interactions...
from U(1), respectively, all of which are massless.
In the
Standard ModelThe Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...
, the
{{SubatomicParticleThe W and Z bosons are the elementary particles that mediate the weak interaction; their symbols are , and . The W bosons have a positive and negative electric charge of 1 elementary charge respectively and are each other's antiparticle. The Z boson is electrically neutral and its own...
, and the photon, are produced by the
spontaneous symmetry breakingSpontaneous symmetry breaking is the process by which a system described in a theoretically symmetrical way ends up in an apparently asymmetric state....
of the
electroweak symmetry from
SU(2) ×
U(1)
Y to
U(1)
em, caused by the
Higgs mechanismIn particle physics, the Higgs mechanism is the process in which gauge bosons in a gauge theory can acquire non-vanishing masses through absorption of Nambu-Goldstone bosons arising in spontaneous symmetry breaking....
(see also
Higgs bosonThe Higgs boson is a hypothetical massive elementary particle that is predicted to exist by the Standard Model of particle physics. Its existence is postulated as a means of resolving inconsistencies in the Standard Model...
).
U(1)
Y and
U(1)
em are different copies of
U(1); the
generatorIn mathematics, the expressions generator, generate, generated by and generating set can have several closely related technical meanings:...
of
U(1)
em is given by
Q =
Y/2 +
I3, where
Y is the generator of
U(1)
Y (called the
weak hyperchargeThe weak hypercharge in particle physics is a conserved quantum number relating the electrical charge and the third component of weak isospin, and is similar to the Gell-Mann–Nishijima formula for the hypercharge of strong interactions...
), and
I3 is one of the
SU(2) generators (a component of
weak isospinIn particle physics, weak isospin is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol T or I with the third component written as Tz, T3, Iz or I3...
).
The spontaneous symmetry breaking causes the {{SubatomicParticle|W boson0}} and B
0 bosons to coalesce together into two different bosons - the {{SubatomicParticle|Z boson0}} boson, and the photon (γ) as follows:
-
Where θW is the weak mixing angle. The axes representing the particles have essentially just been rotated, in the ({{SubatomicParticle|W boson0}}, B0) plane, by the angle θW. This also introduces a discrepancy between the mass of the {{SubatomicParticle|Z boson0}} and the mass of the {{SubatomicParticle|W boson+-}} particles (denoted as MZ and MW, respectively);
The distinction between electromagnetism and the weak force arises because there is a (nontrivial) linear combination of Y and I3 that vanishes for the Higgs boson (it is an eigenstate of both Y and I3, so the coefficients may be taken as −I3 and Y): U(1)em is defined to be the group generated by this linear combination, and is unbroken because it does not interact with the Higgs.
Before Electroweak Symmetry Breaking
The LagrangianThe Lagrangian, L, of a dynamical system is a function that summarizes the dynamics of the system. It is named after Joseph Louis Lagrange. The concept of a Lagrangian was originally introduced in a reformulation of classical mechanics by Irish mathematician William Rowan Hamilton known as...
for the electroweak interactions is divided into four parts before electroweak symmetry breaking
The g term describes the interaction between the three W particles and the B particle.
The f term gives the kinetic term for the Standard Model fermions. The interaction of the gauge bosons and the fermions are through the covariant derivativeIn mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way of introducing and working with a connection on a manifold by means of a differential operator, to be contrasted with the approach given...
.
The h term describes the Higgs field F.
The y term gives the Yukawa interactionIn particle physics, Yukawa's interaction, named after Hideki Yukawa, is an interaction between a scalar field \phi and a Dirac field \Psi of the typeV \approx g\bar\Psi \phi \Psi or g \bar \Psi \gamma^5 \phi \Psi ....
that generates the fermion masses after the Higgs acquires a vacuum expectation value.
After Electroweak Symmetry Breaking
The Lagrangian reorganizes itself after the Higgs boson acquires a vacuum expectation value. Due to its complexity, this Lagrangian is best described by breaking it up into several parts as follows.
The kinetic term 
contains all the quadratic terms of the Lagrangian, which include the dynamic terms (the partial derivatives) and the mass terms (conspicuously absent from the Lagrangian before symmetry breaking)
where the sum runs over all the fermions of the theory (quarks and leptons), and the fields 
, 
, 
, and 
are given as
, (replace X by the relevant field, and fabc with the structure constants for the gauge group).
The neutral current 
and charged current 
components of the Lagrangian contain the interactions between the fermions and gauge bosons.
,
where the electromagnetic current 
and the neutral weak current 
are
,
and
and 
are the fermions' electric charges and weak isospin.
The charged current part of the Lagrangian is given by
contains the Higgs three-point and four-point self interaction terms.
contains the Higgs interactions with gauge vector bosons.
contains the gauge three-point self interactions.
contains the gauge four-point self interactions
and 
contains the Yukawa interactions between the fermions and the Higgs field.
See also
- Fundamental forces
- Formulation of the standard model
This is a detailed description of the standard model of particle physics. It describes how the leptons, quarks, gauge bosons and the Higgs particle fit together...
- Weinberg angle
The Weinberg angle or weak mixing angle is a parameter in the Weinberg–Salam theory of the electroweak interaction, and is usually denoted as θW...
General readers
Conveys much of the Standard ModelThe Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...
with no formal mathematics. Very thorough on the weak interaction.