A. S. Wightman, IAMP meeting, London July 2000.

Arthur Wightman founded modern mathematical physics with his work from about 1954 on the formulation of quantum field theory. He did not find the only work then available in book form, that of Heitler, to be very convincing. He decided that a deeper use of mathematics is needed, and formulated the Wightman axioms of relativistic quantum field theory, inspired by the idea that the theory should be a development of Wigner's relativistic quantum theory to the case when local fields are present.

Wightman introduced the idea that that field should be a distribution in the sense of L. Schwartz; in this, he was aided and abetted by L. Garding. I was introduced to Wightman's paper, 1956, by P. K. Roy, then, in 1957 like me, a Ph. D. student of Abdus Salam at Imperial College. I had asked Salam "what IS a quantised field", and received the answer "Good; I was afraid you would ask me something I did not know. A quantised field, phi(x) at the point x of space-time, is that operator assigned by the physicist using the correspondence principle, to the classical field phi at the point x". I went away thinking about this; then I realised that what I needed was a statement of WHICH operator is assigned by the physicist. I complained to P. K. Roy, who said that I should read Wightman's paper.

Under the influence of Wightman, schools of mathematical physics
began to appear; Ruelle in Belgium, and R. Jost
in Zurich, were the first. One by one, various fields of theoretical
physics were subjected to the rigorous treatment. The theory of quantised
fields itself became almost mathematics, after the publication of the book I wrote with Wightman, and Jost's own [**The
General Theory of Quantised Fields**, *Amer. Math. Soc.* 1965].

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© by Ray Streater 12/4/2000.