Introduction to superanalysis

Author(s)

• Berezin, F. A. (Feliks Aleksandrovich)
• Kirillov, Aleksandr Aleksandrovich

Bibliographic Information

Introduction to superanalysis

Felix Alexandrovich Berezin ; edited by A.A. Kirillov ; translated from the Russian by J. Niederle and R. Kotecký ; English translation edited and revised by Dimitri Leites

（Mathematical physics and applied mathematics, v. 9）

D. Reidel , Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers, c1987

Other Title

Superanalysis

Note

Part 1 is translation of: Vvedenie v algebru i analiz s antikommutirui︠u︡shchimi peremennymi

Includes bibliographies

Includes index

List of F. A. Berezin's published works: p. 414-417

Description and Table of Contents

Description

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.

Table of Contents

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.

by "Nielsen BookData"

Details

• NCID: BA00777849
• ISBN:
  • 9027716684
• LCCN: 87016293
• Country Code: ne
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Dordrecht,Norwell, MA
• Pages/Volumes: xii, 424 p.
• Size: 23 cm
• Classification:
  • LCC : QA300
  • DC19 : 530.15/5
• Subject Headings:
  • LCSH : Mathematical analysis
• Parent Bibliography ID:
  • BA0003234X