José Enrique Moyal (‎; 1 October 1910 – 22 May 1998) was an Australian mathematician and mathematical physicist who contributed to

aeronautical engineering Aerospace engineering is the primary field of engineering concerned with the development of aircraft and spacecraft. It has two major and overlapping branches: aeronautical engineering and astronautical engineering. Avionics engineering is s ...

electrical engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems that use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...

and

statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...

, among other fields.Ann Moyal, ''Maverick Mathematician: The Life and Science of J.E. Moyal'', ANU E-press, 2006; ,
accessible online
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Career

Moyal helped establish the phase space formulation of

quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...

in 1949 by bringing together the ideas of

Hermann Weyl Hermann Klaus Hugo Weyl (; ; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist, logician and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, ...

John von Neumann John von Neumann ( ; ; December 28, 1903 – February 8, 1957) was a Hungarian and American mathematician, physicist, computer scientist and engineer. Von Neumann had perhaps the widest coverage of any mathematician of his time, in ...

Eugene Wigner Eugene Paul Wigner (, ; November 17, 1902 – January 1, 1995) was a Hungarian-American theoretical physicist who also contributed to mathematical physics. He received the Nobel Prize in Physics in 1963 "for his contributions to the theory of th ...

, and Hip Groenewold. This formulation is statistical in nature and makes logical connections between

and classical

statistical mechanics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applicati ...

, enabling a natural comparison between the two formulations. Phase space quantization, also known as ''Moyal quantization'', largely avoids the use of operators for quantum mechanical observables prevalent in the canonical formulation. Quantum-mechanical evolution in phase space is specified by a

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 l ...

. Moyal grew up in

Tel Aviv Tel Aviv-Yafo ( or , ; ), sometimes rendered as Tel Aviv-Jaffa, and usually referred to as just Tel Aviv, is the most populous city in the Gush Dan metropolitan area of Israel. Located on the Israeli Mediterranean coastline and with a popula ...

, and attended the Herzliya Hebrew Gymnasium. He studied in Paris in the 1930s, at the École Supérieure d'Electricité, Institut de Statistique, and, finally, at the

Institut Henri Poincaré The Henri Poincaré Institute (or IHP for ''Institut Henri Poincaré'') is a mathematics research institute part of Sorbonne University, in association with the Centre national de la recherche scientifique (CNRS). It is located in the 5th arrondi ...

. His work was carried out in wartime England in the 1940s, while employed at the

de Havilland The de Havilland Aircraft Company Limited (pronounced , ) was a British aviation manufacturer established in late 1920 by Geoffrey de Havilland at Stag Lane Aerodrome Edgware on the outskirts of North London. Operations were later moved to ...

Aircraft company. Moyal was a professor of mathematics at the former School of Mathematics and Physics of

Macquarie University Macquarie University ( ) is a Public university, public research university in Sydney, New South Wales, Australia. Founded in 1964 by the New South Wales Government, it was the third university to be established in the Sydney metropolitan area. ...

, where he was a colleague of John Clive Ward. Previously, he had worked at the

Argonne National Laboratory Argonne National Laboratory is a Federally funded research and development centers, federally funded research and development center in Lemont, Illinois, Lemont, Illinois, United States. Founded in 1946, the laboratory is owned by the United Sta ...

Illinois Illinois ( ) is a U.S. state, state in the Midwestern United States, Midwestern United States. It borders on Lake Michigan to its northeast, the Mississippi River to its west, and the Wabash River, Wabash and Ohio River, Ohio rivers to its ...

. He published pioneering work on stochastic processes.

Personal life

Moyal was married to Susanna Pollack (1912-2000), with whom he had two children, Orah Young (born in Tel Aviv) and David Moyal (born in Belfast). They divorced in 1956. He was married to Ann Moyal from 1962 until his death.

Works

* * J.E. Moyal, "Stochastic Processes and Statistical Physics"

Journal of the Royal Statistical Society The ''Journal of the Royal Statistical Society'' is a peer-reviewed scientific journal of statistics. It comprises three series and is published by Oxford University Press for the Royal Statistical Society. History The Statistical Society of ...

B'', 11, (1949), 150–210.

References

External links

Maverick Mathematician: The Life and Science of J.E. Moyal

Moyal Medal
awarded annually by Macquarie University for research contributions to mathematics, physics or statistics 1910 births 1998 deaths 20th-century Australian mathematicians Australian physicists Australian statisticians Israeli emigrants to Australia Herzliya Hebrew Gymnasium alumni Jewish physicists Academic staff of Macquarie University Mathematical physicists Scientists from Jerusalem Quantum physicists Mandatory Palestine expatriates in France Mandatory Palestine expatriates in the United Kingdom University of Paris alumni {{Physicist-stub

Career

Personal life

Works

See also

References

External links