# Arthur Wightman : biography

**Arthur Strong Wightman** (March 30, 1922 – January 13, 2013)) was an American mathematical physicist. He was one of the founders of the axiomatic approach to quantum field theory, and originated the set of Wightman axioms.

Advised by John Wheeler, his 1949 Princeton doctoral dissertation was entitled *The Moderation and Absorption of Negative Pions in Hydrogen*. His graduate students include Arthur Jaffe, Jerrold Marsden, and Alan Sokal. His work is summarized in the classic concise monograph *PCT, Spin and statistics and all that* written with R F Streater. Its title is a pun on that of the historical satire *1066 and All That* by Sellar and Yeatman. The PCT refers to the combined symmetry of a quantum field theory under P Parity, C charge and T time. Spin and statistics refers to the fact that in quantum field theory it can be proved that spin 1/2 particles obey Fermi-Dirac statistics whereas integer spin 0, 1, 2 particles obey Bose-Einstein statistics.

Wightman was awarded the Henri Poincaré Prize of the International Association of Mathematical Physics in 1997. Until his death, he was a professor emeritus at Princeton.

## Works

- Streater and Arthur Wightman:
*PCT, Spin, Statistics and all that*, Princeton University Press 2000 (1st edn., New York, Benjamin 1964) - Arthur Wightman:
*Quantum field theory in terms of vacuum expectation values*. In:*Physical Review*. vol. 101, 1956, p. 860 - Arthur Wightman and Lars Gårding:
*Fields as operator-valued distributions in relativistic quantum theory*. In:*Arkiv för Fysik*. vol. 28, 1965, pp. 129–184 - Arthur Wightman:
*What is the point of so-called "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*. vol. 19, 1975, p. 983 - Arthur Wightman, Wick and Wigner:
*Intrinsic parity of elementary particles*. In:*Physical Review*. vol. 88, 1952, p. 101 - Arthur Wightman:
*Looking back at Quantum Field Theory*. In:*physica scripta*. vol. 24, 1981, p. 813 - Res Jost:
*To Arthur Wightman*. In:*Communications in mathematical physics*. vol. 132, 1990, p. 1 - Arthur Wightman:
*The theory of quantized fields in the 50s*, in Brown, Dresden, Hoddeson (eds.)*Pions to quarks: particle physics in the 50s*, Cambridge University Press 1989