José Enrique Moyal
Encyclopedia
José Enrique Moyal (born 1 October 1910 in Jerusalem, then in the Ottoman Empire
and soon to devolve to the Mandate for Palestine; died 22 May 1998 in Canberra
, Australia
) was a mathematical physicist who contributed to aeronautical engineering, electrical engineering
and statistics
, among other fields. He helped to establish the phase space
formulation of quantum mechanics
in 1949 by bringing together the ideas of Hermann Weyl
, John von Neumann
, Eugene Wigner, and Hip Groenewold
.
This formulation is statistical in nature and makes logical connections between quantum mechanics
and classical statistical mechanics
, enabling a natural comparison between the two formulations.
Weyl quantization
is a synonym for "Moyal Quantization", or "Phase Space Quantization," and largely avoids use of operators for quantum mechanical observables prevalent in the canonical formulation. Quantum-mechanical evolution in phase space is specified by a Moyal bracket
.
He was a professor of mathematics at Macquarie University
and a colleague of John Clive Ward
at the former School of Mathematics and Physics, having previously worked at Argonne National Laboratory
in Illinois
.
Ottoman Empire
The Ottoman EmpireIt was usually referred to as the "Ottoman Empire", the "Turkish Empire", the "Ottoman Caliphate" or more commonly "Turkey" by its contemporaries...
and soon to devolve to the Mandate for Palestine; died 22 May 1998 in Canberra
Canberra
Canberra is the capital city of Australia. With a population of over 345,000, it is Australia's largest inland city and the eighth-largest city overall. The city is located at the northern end of the Australian Capital Territory , south-west of Sydney, and north-east of Melbourne...
, Australia
Australia
Australia , officially the Commonwealth of Australia, is a country in the Southern Hemisphere comprising the mainland of the Australian continent, the island of Tasmania, and numerous smaller islands in the Indian and Pacific Oceans. It is the world's sixth-largest country by total area...
) was a mathematical physicist who contributed to aeronautical engineering, electrical engineering
Electrical engineering
Electrical 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...
and statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, among other fields. He helped to establish the phase space
Phase space
In mathematics and physics, a phase space, introduced by Willard Gibbs in 1901, is a space in which all possible states of a system are represented, with each possible state of the system corresponding to one unique point in the phase space...
formulation of quantum mechanics
Quantum mechanics
Quantum 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...
in 1949 by bringing together the ideas of Hermann Weyl
Hermann Weyl
Hermann Klaus Hugo Weyl was a German mathematician and theoretical physicist. Although much of his working life was spent in Zürich, Switzerland and then Princeton, he is associated with the University of Göttingen tradition of mathematics, represented by David Hilbert and Hermann Minkowski.His...
, John von Neumann
John von Neumann
John von Neumann was a Hungarian-American mathematician and polymath who made major contributions to a vast number of fields, including set theory, functional analysis, quantum mechanics, ergodic theory, geometry, fluid dynamics, economics and game theory, computer science, numerical analysis,...
, Eugene Wigner, and Hip Groenewold
Hilbrand J. Groenewold
Hilbrand Johannes Groenewold was a Dutch theoretical physicist who pioneered the largely operator-free formulation of quantum mechanics in phase space known as phase-space quantization....
.
This formulation is statistical in nature and makes logical connections between quantum mechanics
Quantum mechanics
Quantum 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 classical statistical mechanics
Statistical mechanics
Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
, enabling a natural comparison between the two formulations.
Weyl quantization
Weyl quantization
In mathematics and physics, in the area of quantum mechanics, Weyl quantization is a method for systematically associating a "quantum mechanical" Hermitian operator with a "classical" kernel function in phase space invertibly...
is a synonym for "Moyal Quantization", or "Phase Space Quantization," and largely avoids use of operators for quantum mechanical observables prevalent in the canonical formulation. Quantum-mechanical evolution in phase space is specified by a Moyal bracket
Moyal bracket
In physics, the Moyal bracket is the suitably normalized antisymmetrization of the phase-space star product.The Moyal Bracket was developed in about 1940 by José Enrique Moyal, but Moyal only succeeded in publishing his work in 1949 after a lengthy dispute with Dirac...
.
He was a professor of mathematics at Macquarie University
Macquarie University
Macquarie University is an Australian public teaching and research university located in Sydney, with its main campus situated in Macquarie Park. Founded in 1964 by the New South Wales Government, it was the third university to be established in the metropolitan area of Sydney...
and a colleague of John Clive Ward
John Clive Ward
John Clive Ward , was a British-Australian physicist. His most famous creation was the Ward-Takahashi identity, originally known as "Ward Identity" . This celebrated result, in quantum electrodynamics, was inspired by a conjecture of Dyson and was disclosed in a one-half page letter typical of...
at the former School of Mathematics and Physics, having previously worked at Argonne National Laboratory
Argonne National Laboratory
Argonne National Laboratory is the first science and engineering research national laboratory in the United States, receiving this designation on July 1, 1946. It is the largest national laboratory by size and scope in the Midwest...
in Illinois
Illinois
Illinois is the fifth-most populous state of the United States of America, and is often noted for being a microcosm of the entire country. With Chicago in the northeast, small industrial cities and great agricultural productivity in central and northern Illinois, and natural resources like coal,...
.
Works
- J.E. Moyal, "Quantum mechanics as a statistical theory", "Proceedings of the Cambridge Philosophical Society." 45 (1949), 99-124.
- J.E. Moyal, "Stochastic Processes and Statistical Physics"Journal of the Royal Statistical SocietyJournal of the Royal Statistical SocietyThe Journal of the Royal Statistical Society is a series of three peer-reviewed statistics journals published by Blackwell Publishing for the London-based Royal Statistical Society.- History :...
B, 11, (1949),150-210.
Obituaries
- J. Gani, "Obituary: José Enrique Moyal," "J. Appl. Probab." 35 (1998), no. 4, 1012–1017.
- M.S. BartlettM. S. BartlettMaurice Stevenson Bartlett FRS was an English statistician who made particular contributions to the analysis of data with spatial and temporal patterns...
, "José Enrique Moyal," "The Statistician," 48 (1998), 273–274. (Bartlett acknowledges how much he gained from Moyal's wide knowledge of the European literature on probability.)
External links
- Obituary by Alan McIntosh and photographs
- Moyal Medal awarded annually by Macquarie University for research contributions to mathematics, physics or statistics
- José Enrique Moyal from the Mathematics Genealogy ProjectMathematics Genealogy ProjectThe Mathematics Genealogy Project is a web-based database for the academic genealogy of mathematicians. As of September, 2010, it contained information on approximately 145,000 mathematical scientists who contribute to "research-level mathematics"...
See also
- Moyal bracketMoyal bracketIn physics, the Moyal bracket is the suitably normalized antisymmetrization of the phase-space star product.The Moyal Bracket was developed in about 1940 by José Enrique Moyal, but Moyal only succeeded in publishing his work in 1949 after a lengthy dispute with Dirac...
- Weyl quantizationWeyl quantizationIn mathematics and physics, in the area of quantum mechanics, Weyl quantization is a method for systematically associating a "quantum mechanical" Hermitian operator with a "classical" kernel function in phase space invertibly...
- Wigner quasi-probability distributionWigner quasi-probability distributionThe Wigner quasi-probability distribution is a quasi-probability distribution. It was introduced by Eugene Wigner in 1932 to study quantum corrections to classical statistical mechanics...