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.[1] With his rigorous treatment of quantum field theories, he promoted research on various aspects of modern
mathematical physics.[2]
Wightman has been married twice. His first wife, Anna-Greta Larsson, was an artist and photographer and died early. They had a daughter, Robin, who also died prematurely. The second wife was the Bulgarian translator Ludmilla Popova Wightman. Wightman died on January 13, 2013, in
Princeton, in
New Jersey.[7]
Scientific career
Already during his undergraduate studies, Arthur Wightman had close contacts with the mathematics department in Princeton. Together with the mathematician
John Tate, Wightman was engaged in the work on the Lorentz and
Poincaré groups representations.[8]
In the 1950s, he introduced his
Wightman axioms as a mathematical foundation to relativistic quantum field theory. Quantum fields are treated as
distributions in space-time. The
Hilbert space carries a unitary representation of the Poincaré group under which the field operators transform covariantly. Wightman's paper with D. Hall reported to a theorem that stated that the expectation value of the product of two fields, , could be
analytically continued to all separations .[9]: 425 Using this,
Res Jost was able to derive the
PCT and the
spin-statistics theorems, as shown in Wightman's and
Streater's book.[10] Together with Eugene Wigner and
Gian-Carlo Wick, he introduced
superselection rules and studied the representations of commutator and anti-commutator algebras with the mathematician
Lars Gårding.[11]
Wightman, Arthur S. (1967). Introduction to some aspects of the relativistic dynamics of quantized fields, Cargese Lectures in Theoretical Physics. Gordon and Breach Science Publishers.
Wightman, Arthur S. (1977). "Should We Believe in Quantum Field Theory?". 15th Erice School of Subnuclear Physics: The Why's of Subnuclear Physics. pp. 983–1025.
Wick, Gian Carlo; Wightman, Arthur S.; Wigner, Eugene P. (1952). "The intrinsic parity of elementary particles". Physical Review. 88 (1): 101–105.
Bibcode:
1952PhRv...88..101W.
doi:
10.1103/PhysRev.88.101.
Wightman, Arthur S. (1981). "Looking back at quantum field theory". Physica Scripta. 24 (5): 813–816.
doi:
10.1088/0031-8949/24/5/001.
^Jaffe, Arthur; Simon, Barry (January 2013).
"Arthur Strong Wightman (1922–2013)"(PDF). News Bulletin, International Association of Mathematical Physics: 34–36.
^Duck, Ian; Sudarshan, Ennackel Chandy George; Sudarshan, E. C. G. (1998). Pauli and the spin-statistics theorem (1. reprint ed.). Singapore: World Scientific.
ISBN978-981-02-3114-9.
^Streater, Raymond F.; Wightman, Arthur S. (1989). PCT, spin and statistics, and all that.
ISBN978-0691070629.
Jaffe, Arthur; Simon, Barry (January 2013).
"Arthur Strong Wightman (1922–2013)"(PDF). News Bulletin, International Association of Mathematical Physics: 34–36.