Felix Berezin

The following sections are included:

• FOREWORD

• CONTENTS

Within the path integral approach quantum field theory can be formulated as an integral over the superspace of fields. The Berezin integral is the crucial element in this construction. Replacing an infinite-dimensional supermanifold of fields by an ordinary supermanifold we get a nice toy model of quantum field theory. In this article I motivate the origin of the Berezin integral and trace some of its applications, up to the Batalin–Vilkovisky formalism. The latter was developed as a method for determining the ghost structure in such theories as gravity and supergravity, whose Hamiltonian formalism has constraints not related to a Lie algebra action.

The following sections are included:

• What He Achieved in Science

• Early Years

• The First Period of Work at the University

• The Last Period

• F. A. Berezin's Social and Political Status and Position at the Department

• References

Please refer to full text.

The following sections are included:

• Beginning of the End

• Moscow – Krasnoyarsk

• Krasnoyarsk – Magadan

• Magadan – Seymchan – Magadan

• Magadan – Moscow

• The End and Beginning

Please refer to full text.

These are personal notes concerning my acquaintance and relationship with F. A. Berezin …

Berezin's departure from this world was unexpected and mysterious. There is an element of mystery in any death, but Alik's death, far away from Moscow, in a geological party, where there were no friends, under circumstances that remain unclear, was a strange kind of disappearance. I remember the moment when I was told about it, and the overwhelming feeling of disbelief …

This paper is about my very good friend Felix Berezin and his mathematical works. In particular, I discuss the connection of his less known paper on projective representations of the current groups with my paper with I.M. Gelfand and M.I. Graev on multiplicative integral of representations. Ten years ago I wrote my first “Berezin note.” It will be reprinted in this Collection. However, when I looked at it now I found many things about Alik which I did not mention but which should have been mentioned. The reader will find some of them below, while some others are left for future publications. Recently a memorial volume dedicated to Berezin's 75-anniversary was released in St. Petersburg. It contains mathematical papers of his friends and followers and was published in 2006 in Russian as Zapiski Nauchnykh Seminarow POMI, v. 331: Theory of Representations, Dynamical Systems and Combinatorics, XIV, Ed. A. Vershik. The English version will become available as an issue of Journal of Mathematical Science, v. 141, February 2007 (Springer-Verlag, Berlin). The text below coincides in part with my preface in that Volume.

These notes make no claim to completeness and no attempts at any generalizations. They are simply the reminiscences of a close friend …

The following sections are included:

• Acquaintance in Absentia

• How we Wound up in Siberia

• I Meet Berezin for the First Time

• A Seminar at the Institute of Physical Problems

• The Hassle with my Thesis Defense; Berezin is my Opponent

• Kolyma Stories

• Novosibirsk 1979, Akademgorodok, Thesis Defense

• 1980 and Later

Please refer to full text.

The following sections are included:

• Introduction

• From the history of Berezin's inequalities

• References

The following sections are included:

• Acceptance of new students

• Admission to the Graduate School

• Administration's treatment of the faculty. Admitting new students

• Scientific policy

Please refer to full text.

The following sections are included:

• From Wikipedia, the free encyclopedia