Life and work
Wightman studied at Yale University (Bachelor in 1942, then he was there 1943/44, Instructor and served in the U.S. Navy ) and was with John Archibald Wheeler at Princeton University with a nuclear physics topic doctorate in 1949 (interaction of negative pions with hydrogen). He had actually intended to do a doctorate at Eugene Wigner, but this time was mainly at the Oak Ridge National Laboratory. He was then at Princeton from 1949 first. Than Instructor and then as a professor Since 1971 he was there Thomas D. Jones Professor of Mathematical Physics. He became Professor Emeritus in 1992. 1951/52 and 1956/57, he was a visiting scholar at the University of Copenhagen ( Niels Bohr Institute, during this time he worked in particular with Gunnar Källen and Lars Garding in the near Lund together ), 1957 at the University of Paris and 1963 /64 and 1968 / 69 at IHES, with which he helped at the invitation of its founders, to establish a program for mathematical physics. 1977/78 he was a visiting professor at the Ecole Polytechnique and 1982 at the University of Adelaide. He led a series of summer schools in mathematical physics with Giorgio Velo in Erice and taught regularly at the summer schools of Cargese, Les Houches and Varenna ( Enrico Fermi School).
Even in his student days he had close contacts with the Mathematics Department at Princeton and engaged, together with the friend, the mathematician John T. Tate, with the work on the representation of the Lorentz and Poincaré group by Eugene Wigner and Valentine Bargmann. Wightman was until his retirement Professor at Princeton University, most recently as Thomas D. Jones Professor in both the mathematical and in the physics department.
In the 1950s he gave the relativistic quantum field theory, a mathematical basis with the introduction of its Wightman axioms. Quantum fields are treated therein as distributions in the space-time whose values are operators in a Hilbert space, the commutator or anti - commutator relationships meet ( which vanish for space-like distances ). The Hilbert space carries a unitary representation of the Poincaré group under the transform the covariant field operators. Res Jost could allow the PCT and spin-statistics theorems derived, as shown in Wightmans book with Ray Streater. With Eugene Wigner and Gian- Carlo Wick, he led a super- selection rules ( super selection rules) and examined with the mathematician Lars Garding the representations of commutator and anti- commutator algebras.
Wightman was with his treatment of quantum field theories essential to the establishment of mathematical physics.
His doctoral include Silvan Schweber, Eduard Prugovecki, 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 of Mathematical Physics. Since 1970 he is a member of the National Academy of 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 held the Gibbs Lecture (1976).
He was associate editor of the Communications in Mathematical Physics and supported its creation. He published a series of books by Princeton University Press and was in its governing body. At his death, the flag of Princeton University was set three days at half-mast.
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. In his second marriage he was married to Bulgarian translator Ludmilla Popova Wightman.