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Introduction to Superanalysis : Mathematical Physics & Applied Mathematics - F. A. Berezin

Introduction to Superanalysis

Mathematical Physics & Applied Mathematics

By: F. A. Berezin, A. A. Kirillov, J. Niederle (Translator), R. Kotecky (Translator)

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Published: 31st July 1987
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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 (c) 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.

1. Grassmann Algebra.- 2. Superanalysis.- 3. Linear Algebra in Z2-Graded Spaces.- 4. Supermanifolds in General.- 5. Lie Superalgebras.- 1. Lie Superalgebras.- 2. Lie Supergroups.- 3. Laplace-Casimir Operators (General Theory).- 4. Radial Parts of the Laplace Operators on the Lie Supergrouups U(p, q) and C(m, n).- 5. Construction of Representations of Lie Supergroups U(p, q) and C(m, n).- Appendix 1. Particle Spin Dynamics as the Grassmann Variant of Classical Mechanics.- Appendix 2. Supersymmetry and Supergravity by V. I. Ogievetsky.- Supplement. List of F. A. Berezin's Published Works.

ISBN: 9789027716682
ISBN-10: 9027716684
Series: Mathematical Physics & Applied Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 424
Published: 31st July 1987
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 24.13 x 16.51  x 3.18
Weight (kg): 0.79