José Enrique Moyal ( he, יוסף הנרי מויאל‎; 1 October 1910 – 22 May 1998) was an Australian mathematician and

mathematical physicist Mathematical physics refers to the development of mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the developmen ...

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 sim ...

, electrical engineering and statistics, 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 The phase-space formulation of quantum mechanics places the position ''and'' momentum variables on equal footing in phase space. In contrast, the Schrödinger picture uses the position ''or'' momentum representations (see also position and mome ...

quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistr ...

in 1949 by bringing together the ideas of Hermann Weyl,

John von Neumann John von Neumann (; hu, Neumann János Lajos, ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest cove ...

Eugene Wigner Eugene Paul "E. P." Wigner ( hu, Wigner Jenő Pál, ; 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 co ...

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

and classical statistical mechanics, 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. Moyal grew up in

Tel Aviv Tel Aviv-Yafo ( he, תֵּל־אָבִיב-יָפוֹ, translit=Tēl-ʾĀvīv-Yāfō ; ar, تَلّ أَبِيب – يَافَا, translit=Tall ʾAbīb-Yāfā, links=no), often referred to as just Tel Aviv, is the most populous city in the ...

, and attended the

Herzliya Hebrew Gymnasium The Herzliya Hebrew Gymnasium ( he, הַגִּימְנַסְיָה הָעִבְרִית הֶרְצְלִיָּה, ''HaGymnasia HaIvrit Herzliya'', Also known as ''Gymnasia Herzliya''), originally known as HaGymnasia HaIvrit (lit. Hebrew High Scho ...

. 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 arrond ...

. His work was carried out in wartime England in the 1940s, while employed at the de Havilland Aircraft company. Moyal was a professor of mathematics at the former School of Mathematics and Physics of Macquarie University, where he was a colleague of

John Clive Ward John Clive Ward, (1 August 1924 – 6 May 2000) was a British-Australian physicist. He introduced the Ward–Takahashi identity, also known as "Ward Identity" (or "Ward's Identities"). Andrei Sakharov said Ward was one of the titans of q ...

. Previously, he had worked at the Argonne National Laboratory in

Illinois Illinois ( ) is a state in the Midwestern United States. Its largest metropolitan areas include the Chicago metropolitan area, and the Metro East section, of Greater St. Louis. Other smaller metropolitan areas include, Peoria and Rockf ...

. 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 Wiley for the Royal Statistical Society. History The Statistical Society of London was founded ...

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 Macquarie University faculty Mathematical physicists People from Jerusalem Quantum physicists Mandatory Palestine expatriates in France Mandatory Palestine expatriates in the United Kingdom {{Physicist-stub

Career

Personal life

Works

See also

References

External links