Felix Berezin

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Felix Berezin Life And Death Of The Mastermind Of Supermathematics

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Author : Misha Shifman
language : en
Publisher: World Scientific
Release Date : 2007-04-27

Felix Berezin Life And Death Of The Mastermind Of Supermathematics written by Misha Shifman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-27 with Mathematics categories.

Felix Berezin was 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 anticommuting Grassmann variables that he introduced in the 1960s 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.This book features a masterfully written memoir by Berezin's widow, Elena Karpel, who narrates a remarkable account of Berezin's life and his struggle for survival under the totalitarian Soviet regime. Supplemented with recollections by his close friends and colleagues, Berezin's accomplishments in mathematics, his novel ideas and breakthrough works, are reviewed in two articles written by Andrei Losev and Robert Minlos.

Felix Berezin

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Author : Mikhail A. Shifman
language : en
Publisher: World Scientific
Release Date : 2007

Felix Berezin written by Mikhail A. Shifman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

Felix Berezin was 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 anticommuting Grassmann variables that he introduced in the 1960s 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. This book features a masterfully written memoir by BerezinOCOs widow, Elena Karpel, who narrates a remarkable account of BerezinOCOs life and his struggle for survival under the totalitarian Soviet regime. Supplemented with recollections by his close friends and colleagues, BerezinOCOs accomplishments in mathematics, his novel ideas and breakthrough works, are reviewed in two articles written by Andrei Losev and Robert Minlos."

Introduction To Superanalysis

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Author : F.A. Berezin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-09

Introduction To Superanalysis written by F.A. Berezin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-09 with Science categories.

TO SUPERANAL YSIS Edited by A.A. KIRILLOV Translated from the Russian by J. Niederle and R. Kotecky English translation edited and revised by Dimitri Leites SPRINGER-SCIENCE+BUSINESS MEDIA, B.V. Library of Congress Cataloging-in-Publication Data Berezin, F.A. (Feliks Aleksandrovich) Introduction to superanalysis. (Mathematical physics and applied mathematics; v. 9) Part I is translation of: Vvedenie v algebru i analiz s antikommutirurushchimi peremennymi. Bibliography: p. Includes index. 1. Mathetical analysis. I. Title. II. Title: Superanalysis. III. Series. QA300. B459 1987 530. 15'5 87-16293 ISBN 978-90-481-8392-0 ISBN 978-94-017-1963-6 (eBook) DOI 10. 1007/978-94-017-1963-6 All Rights Reserved © 1987 by Springer Science+Business Media Dordrecht Originally published by D. Reidel Publishing Company, Dordrecht, Holland in 1987 No part of the material protected by this copyright notice may be reproduced in whole or in part or utilized in any form or by any means electronic or mechanical including photocopying recording or storing in any electronic information system without first obtaining the written permission of the copyright owner. CONTENTS EDITOR'S FOREWORD ix INTRODUCTION 1 1. The Sources 1 2. Supermanifolds 3 3. Additional Structures on Supermanifolds 11 4. Representations of Lie Superalgebras and Supergroups 21 5. Conclusion 23 References 24 PART I CHAPTER 1. GRASSMANN ALGEBRA 29 1. Basic Facts on Associative Algebras 29 2. Grassmann Algebras 35 3. Algebras A(U) 55 CHAPTER 2. SUPERANAL YSIS 74 1. Derivatives 74 2. Integral 76 CHAPTER 3. LINEAR ALGEBRA IN Zz-GRADED SPACES 90 1.

The Schr Dinger Equation

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Author : F.A. Berezin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

The Schr Dinger Equation written by F.A. Berezin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This volume deals with those topics of mathematical physics, associated with the study of the Schrödinger equation, which are considered to be the most important. Chapter 1 presents the basic concepts of quantum mechanics. Chapter 2 provides an introduction to the spectral theory of the one-dimensional Schrödinger equation. Chapter 3 opens with a discussion of the spectral theory of the multi-dimensional Schrödinger equation, which is a far more complex case and requires careful consideration of aspects which are trivial in the one-dimensional case. Chapter 4 presents the scattering theory for the multi-dimensional non-relativistic Schrödinger equation, and the final chapter is devoted to quantization and Feynman path integrals. These five main chapters are followed by three supplements, which present material drawn on in the various chapters. The first two supplements deal with general questions concerning the spectral theory of operators in Hilbert space, and necessary information relating to Sobolev spaces and elliptic equations. Supplement 3, which essentially stands alone, introduces the concept of the supermanifold which leads to a more natural treatment of quantization. Although written primarily for mathematicians who wish to gain a better awareness of the physical aspects of quantum mechanics and related topics, it will also be useful for mathematical physicists who wish to become better acquainted with the mathematical formalism of quantum mechanics. Much of the material included here has been based on lectures given by the authors at Moscow State University, and this volume can also be recommended as a supplementary graduate level introduction to the spectral theory of differential operators with both discrete and continuous spectra. This English edition is a revised, expanded version of the original Soviet publication.

Quantum Field Theory Ii

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Author : Misha Shifman
language : en
Publisher: World Scientific
Release Date : 2019-03-12

Quantum Field Theory Ii written by Misha Shifman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-12 with Science categories.

This textbook grew out of lecture notes the author used in delivering a quantum field theory (QFT) course for students (both in high energy physics and condensed matter) who already had an initial exposure to the subject.It begins with the path integral method of quantization presented in a systematic and clear-cut manner. Perturbation theory is generalized beyond tree level, to include radiative corrections (loops). Renormalization procedures and the Wilsonian renormalization group (RG flow) are discussed, asymptotic freedom of non-Abelian gauge theories is derived, and some applications in Quantum Chromodynamics (QCD) are considered, with a brief digression into the Standard Model (SM). The SM case requires a study of the spontaneous breaking of gauge symmetry, a phenomenon which would be more appropriate to call 'Higgsing of the gauge bosons.' Other regimes attainable in gauge theories are explained as well. In the condensed matter part, the Heisenberg and Ising model are discussed. The present textbook differs from many others in that it is relatively concise and, at the same time, teaches students to carry out actual calculations which they may encounter in QFT-related applications.

The Method Of Second Quantization

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Author : F.A. Berazin
language : en
Publisher: Elsevier
Release Date : 2012-12-02

The Method Of Second Quantization written by F.A. Berazin and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Science categories.

The Method of Second Quantization deals with the method of second quantization and its use to solve problems of quantum mechanics involving an indefinite number of particles, mainly in field theory and quantum statistics. Topics covered include operations on generating functionals; linear canonical transformations; quadratic operators; and Thirring's four-fermion model. State spaces and the simplest operators are also described. This book is comprised of four chapters and begins with an overview of the method of second quantization and the relevant notations. The first chapter focuses on the connections between vectors and functionals and between operators and functionals, together with fundamental rules for operating on functionals. The reader is then introduced to the so-called quadratic operators and the linear canonical transformations closely connected with them. Quadratic operators reduced and not reduced to normal form are considered. The final chapter discusses the Thirring model, the simplest relativistically invariant model in quantum field theory, and explains why it includes infinities. This monograph will be of value to students and practitioners of mathematical physics.

Topics In Statistical And Theoretical Physics

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Author : R. L. Dobrushin
language : en
Publisher: American Mathematical Soc.
Release Date : 1996

Topics In Statistical And Theoretical Physics written by R. L. Dobrushin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematical physics categories.

Mathematical Cultures

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Author : Brendan Larvor
language : en
Publisher: Birkhäuser
Release Date : 2016-05-25

Mathematical Cultures written by Brendan Larvor and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-25 with Mathematics categories.

This collection presents significant contributions from an international network project on mathematical cultures, including essays from leading scholars in the history and philosophy of mathematics and mathematics education.​ Mathematics has universal standards of validity. Nevertheless, there are local styles in mathematical research and teaching, and great variation in the place of mathematics in the larger cultures that mathematical practitioners belong to. The reflections on mathematical cultures collected in this book are of interest to mathematicians, philosophers, historians, sociologists, cognitive scientists and mathematics educators.

Toeplitz Matrices And Operators

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Author : Nikolaï Nikolski
language : en
Publisher: Cambridge University Press
Release Date : 2020-01-02

Toeplitz Matrices And Operators written by Nikolaï Nikolski and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-02 with Mathematics categories.

A friendly introduction to Toeplitz theory and its applications throughout modern functional analysis.

The Supersymmetric World

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Author : G. L. Kane
language : en
Publisher: World Scientific
Release Date : 2000

The Supersymmetric World written by G. L. Kane and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Science categories.

The story of the discovery of supersymmetry is a fascinating one, unlike that of any other major development in the history of science. This engaging book presents a view of the process, mainly in the words of people who participated. It combines anecdotal descriptions and personal reminiscences with more technical accounts of the trailblazers, covering the birth of the theory and its first years ? the origin of the idea, four-dimensional field theory realization, and supergravity. The eyewitnesses convey to us the drama of one of the deepest discoveries in theoretical physics in the 20th century. This book will be equally interesting and useful to young researchers in high energy physics and to mature scholars ? physicists and historians of science.