Arthur Wightman

Arthur Strong Wightman (born March 30, 1922 in Rochester , New York , USA ; † January 13, 2013 in Edison , New Jersey , USA ) was an American physicist who studied mathematical physics.

life and work

Wightman studied at Yale University (Bachelor in 1942, then he was there 1943/44 instructor and served in the US Navy) and received his doctorate in 1949 under John Archibald Wheeler at Princeton University with a nuclear physics topic (interaction of negative pions with hydrogen). He had actually intended to do his PhD with Eugene Wigner , but at the time he was mainly at the Oak Ridge National Laboratory . He was then in Princeton, first from 1949 as an instructor and then as a professor. Since 1971 he was there Thomas D. Jones Professor of Mathematical Physics. In 1992 he became professor emeritus there. 1951/52 and 1956/57 he was a visiting researcher at the University of Copenhagen (Niels Bohr Institute, during this time he worked in particular with Gunnar Källén and Lars Gårding in nearby Lund), 1957 at the University of Paris and 1963/64 and 1968 / 69 at IHES , where he helped set up a program for mathematical physics at the invitation of its founders. In 1977/78 he was visiting professor at the École polytechnique and in 1982 at the University of Adelaide . He led a number of summer schools in mathematical physics with Giorgio Velo in Erice and taught regularly at the summer schools of Cargèse, Les Houches and Varenna (Enrico Fermi School).

Already during his student days he had close contacts to the mathematics department in Princeton and, together with his friend, mathematician John T. Tate , was engaged in the work on the representation of the Lorentz and Poincaré groups by Eugene Wigner and Valentine Bargmann . Wightman was a professor at Princeton University until his retirement, most recently as Thomas D. Jones Professor in both the mathematics and physics faculties.

In the 1950s he gave the relativistic quantum field theory a mathematical basis with the introduction of his Wightman axioms . Quantum fields are treated as distributions in space-time, the values ​​of which are operators in a Hilbert space that satisfy commutator or anti-commutator relationships (which disappear for space-like distances). The Hilbert space bears a unitary representation of the Poincaré group under which the field operators transform covariant. Res Jost was able to derive the PCT and spin statistics theorems , as shown in Wightman's book with Ray Streater . With Eugene Wigner and Gian-Carlo Wick , he introduced super selection rules and examined the representations of commutator and anti-commutator algebras with mathematician Lars Gårding .

With his mathematically exact treatment of quantum field theories, Wightman contributed significantly to the establishment of mathematical physics.

His doctoral students include Silvan Schweber , Eduard Prugovečki , Vincent Rivasseau , Alan Sokal , Arthur Jaffe , Oscar Lanford , Lawrence Schulman , Jerrold Marsden , Barry Simon , Eugene Speer , Huzihiro Araki , Stephen Fulling, Peter Burgoyne, Richard Ferrell.

In 1969 he received the Dannie Heineman Prize for Mathematical Physics . In 1997 he received the Henri Poincaré Prize at the International Congress for Mathematical Physics. Since 1970 he was a member of the National Academy of Sciences . In 1966 he was elected to the American Academy of Arts and Sciences . In 1962 he was invited speaker at the International Congress of Mathematicians in Stockholm ( Some results on the structure of relativistic quantum field theory ). He gave the Gibbs Lecture (1976).

He was co-editor of Communications in Mathematical Physics and supported its founding. He edited and served on a series of books at Princeton University Press. When he died, the Princeton University flag was hoisted at half-mast for three days.

He was married twice. His first wife, Anna-Greta Larsson, an artist and photographer, died early. With her he had a daughter, Robin, who also died early. His second marriage was to the Bulgarian translator Ludmilla Popova Wightman.

literature

• Streater and Arthur Wightman: PCT, Spin, Statistics and all that , BI Hochschultaschenbuch 1964, as well as English PCT, Spin, Statistics and all that , Princeton University Press 2000 (first New York, Benjamin 1964)
• Arthur Wightman: Quantum field theory in terms of vacuum expectation values . In: Physical Review . Volume 101, 1956, p. 860
• Arthur Wightman and Lars Gårding: Fields as operator-valued distributions in relativistic quantum theory . In: Arkiv för Fysik . Volume 28, 1965, pp. 129-184
• Arthur Wightman: What is the point in axiomatic field theory? . In: Physics Today . September 1969
• Arthur Wightman Introduction to some aspects of the relativistic dynamics of quantized fields , in Maurice Lévy (Ed.) High energy electromagnetic interactions and field theory , Cargèse Summer School 1964, Gordon and Breach, New York 1967
• Arthur Wightman: Should we believe in Quantum Field Theory? . In: Zichichi (Ed.): The Whys of subnuclear physics . In: Ettore Majorana Course . Volume 19, 1975, p. 983
• Arthur Wightman, Wick and Wigner: Intrinsic parity of elementary particles . In: Physical Review . Volume 88, 1952, p. 101
• Arthur Wightman: Looking back at Quantum Field Theory . In: physica scripta . Volume 24, 1981, p. 813
• Res Jost: To Arthur Wightman . In: Communications in mathematical physics . Volume 132, 1990, p. 1
• Arthur Wightman: The theory of quantized fields in the 50s , in Brown, Dresden, Hoddeson (Ed.) Pions to quarks: particle physics in the 50s , Cambridge University Press 1989

Web links

• Ray Streater to Wightman
• Content from Streater, Wightman PCT, Spin, Statistics and all that
• Biography at the APS
• Princeton University Obituary
• Obituary of the Department of Physics (Princeton)
• Barry Simon: In memory of Arthur Strong Wightman, Notices AMS, 2015, no 3

Individual evidence

1. ↑ Involved were also Jurko Glaser , Henri Epstein , Harry Lehmann , Hans Borchers
2. ↑ see obituary: B.Simon, A. Jaffe, Obituary: Arthur Strong Wightman (1922–2013), IAMP News Bulletin, January 2013