Preface to the Special Issue of Jnmp in Memory of F. A. Berezin

Felix Alexandrovich Berezin was born on April 25, 1931 and perished on July 14, 1980 (or several days before) under obscure circumstances while serving — during his summer holidays — as an auxiliary worker for a geological party near the Kolyma river. Wikipedia currently lists several researchers as discoverers of what we now call supersymmetry. Interestingly, Berezin is not even mentioned in this Wikipedia article. However, none of the authors mentioned so far as “pioneers of supersymmetry” qualify as such: Before Wess and Zumino have explained the meaning and importance of supersymmetry none of the earlier discoverers did fully appreciate the meaning and value of their own works, and some of them do not realize its full meaning even now judging by their later works. Contrariwise, Berezin definitely was the first to realize the real value of his discoveries, the fact that he stands on the threshold of the new branch of mathematics, currently referred to as “supermathematics” and guess its possible worthiness for physics, first consciously demonstrated by Wess and Zumino. In early 1960s, Berezin obtained a parallel description of the second quantization for Boze and Fermi particles summarized in his book [1] (where, among other things, Berezin introduces the Berezin integral, and gives a parallel description of the spinor and oscillator representations of, respectively, infinite dimensional orthogonal o(2∞) and symplectic Lie algebras sp(2∞), later rediscovered many times; for an overview of Berezin’s works, see the “scientific part” of [5]). In May 2007, World Scientific published the book “FELIX BEREZIN: Life and Death of the Mastermind of Supermathematics” edited by M. Shifman, [8]. The book consists of contributions of Berezin’s friends, colleagues and students; recollections of Berezin as a person, and some scientific reviews of his results and ideas, their role in mathematical physics and their developments. The core of the book is the skillfully written heart-breaking story of Berezin’s widow, Elena Karpel; and the two Berezin’s letters — to the Rector of Moscow State University and the Moscow Mathematical Society — on the situation in these institutions and in mathematical community in the Soviet Union in general (the problems pointed at in these letters did not lose their timeliness today).