Felix Berezin

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FELIX BEREZIN This book is about Felix Berezin, an outstanding Soviet mathematician who in the 1960s and 70s was the driving force behind the emergence of the branch of mathematics now known as supermathematics. PART The integral over the anticoommuting Grassmann variables he introduced in the 1960s laid the ONE foundation for the path integral formulation of quantum field theory with fermions, the heart of modern supersymmetric field theories and superstrings. The Berezin integral is named for him, as is the closely related construction of the Berezinian which may be regarded as the superanalog of the determinant. PART In a masterfully written memoir Berezin’s widow, Elena Karpel, narrates a remarkable story of TWO Berezin’s life and his struggle for survival in the totalitarian Soviet regime. This story is supple- mented by recollections of Berezin’s close friends and colleagues. Berezin’s acccomplishments of Supermathematics Life and death of the mastermind in mathematics, his novel ideas and breakthrough works, are reviewed in two articles written by Andrei Losev and Robert Minlos. ABOUT M. Shifman is the Ida Cohen Fine Professor of Physics at the University of Minnesota. After receiv- THE EDITOR ing his PhD (1976) from the Institute of Theoretical and Experimental Physics in Moscow he went through all stages of the academic career there. In 1990 he moved to the USA to assume his present position as a member of the William I. Fine Theoretical Physics Institute at the University of Minnesota. In 1997 he was elected as a Fellow of the American Physical Society. He has had the honor of receiving the 1999 Sakurai Prize for Theoretical Particle Physics and the 2006 Julius Edgar Lilienfeld Prize for outstanding contributions to physics. He is the author of several books, over 280 scientific publications, and a number of popular articles and articles on the history of high-energy physics. edited by M. Shifman.

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Мaquette de livre FELIX BEREZIN This book is about Felix Berezin, an outstanding Soviet mathematician who in the 1960s and 70s was the driving force behind the emergence of the branch of mathematics now known as supermathematics. The integral over the anticoomuting Grassman variables he introduced in the 1960’s laid the foundation for the path integral formulation of quantum field theory with fermions, the heart of modern supersymmetric field theories and superstrings. The Berezin integral is named for him as is the closely related construction of the Berezinian which may be regarded as the superanalog of the determinant. In a masterfully written memoir, Berezin’s widow, Elena Karpel, narrates a remarkable story of Berezin’s life and his struggle for survival in the totalitarian Soviet regime. This story is supple- Life and death of the mastermind mented by recollections of Berezin’s close friends and colleagues. Berezin’s accomplishments of Supermathematics in mathematics, his novel ideas and breakthrough works, are reviews in two articles written by Andrei Losev and Robert Minlos. edited by M. Shifman January 29, 2007 11:38 WSPC/Trim Size: 9in x 6in for Proceedings Foreword iii FELIX BEREZIN LIFE AND DEATH OF THE MASTERMIND OF SUPERMATHEMATICS Edited by M. Shifman January 29, 2007 11:38 WSPC/Trim Size: 9in x 6in for Proceedings Foreword iv Copyright page The Editor and Publisher would like to thank the American Math- ematical Society for their kind permission to reprint the articles of V. Maslov, R. Minlos, M. Shubin, N. Vvedenskaya and the ﬁrst article of A. Vershik from the American Mathematical Society Translations, Series 2, Advances in the Mathematical Sciences, Volume 175, 1996.
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Mathematical Education in Universities in the Soviet Union And
sities and research centers or even in other Russian cities Mathematical Education in would regularly come to the seminars too. Seminar par- Universities in the Soviet ticipants would either present their own research or ex- plore the most recent results from abroad considered to be Union and Modern Russia important by seminar leaders. Soviet mathematicians, as well as the rest of the Soviet people, were typically not al- lowed to leave the country; Western mathematicians came Sergei Lando to Russia very rarely, and only a part of Western journals Professor of the Faculty of Mathematics, was available even in the best libraries, often after a serious National Research University time gap. Nevertheless, most of the important research re- Higher School of Economics, sults and theories reached the target audience. Practically Russian Federation all quickly developing domains of mathematics were well [email protected] represented at Mechmat in those years. During that period several Soviet mathematical journals Traditions of mathematical education in Russia on both that published quality papers were widely read all around school and university level, research done by Russian sci- the world, and many Western mathematicians decided to entists and its impact on the development of mathematics is study Russian in order to be able to read the Russian ver- considered by many a unique and valuable part of the world sions of the papers before their translations appear (which cultural heritage. In the present paper, we describe the de- could take some time). Publications in these journals were velopment of mathematical education in Russian universi- considered to be very honorable, and it was not an easy ties after 1955 — a period that proved to be most fruitful.
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