Supermathematics

Abstract: This is a survey of Berezin's work focused on three topics: representation theory, general concept of quantization, and supermathematics.

Abstract: Berezin Integral (A Losev) Felix Berezin. A Brief Scientific Biography (R Minlos) The Last Journey (E Karpel) My Encounters with Felix Berezin (D Gitman) Felix Berezin and His Time (V Paslamodov) Reminiscences of a Close Friend (N Vvedenskaya) Remembering Berezin (V P Maslov) On Berezin (M A Shubin) My Recollections on Berezin (A M Vershik) Creation of Supermathematics (D Leites) Berezin's Seminar (V Golo).

Abstract: In his relatively brief life (he died in an accident before reaching the age of 50), F. A. Berezin succeeded in doing a great deal in mathematics and mathematical physics. Not only did he leave a deep trace in several branches of mathematics that existed before him (group representation theory, the spectral theory of operators, quantum mechanics, statistical physics, constructive quantum field theory), but he also initiated several new concepts, methods, and theories: a general approach to the quantization problem, the construction of the second quantization formalism in terms of functional integrals, which later became the so-called “calculus of symbols” (a forerunner of the theory of pseudo-differential operators), and finally (this was his most important and long nurtured achievement) the theory of supersymmetry and supermanifolds, i.e., what mathematicians now usually call supermathematics. Further we shall discuss all these topics in more detail. Here I would only like to stress that perhaps the most valuable and important characteristic of Berezin’s mathematical life was not his concrete achievements, but the overall stubborn direction of his research, whose main backbone was mathematical physics. He was one of the very few people who transformed mathematical physics into what it � Original publication in Amer. Math. Soc. Transl. (2) 175, Contemporary mathematical physics