Introduction to SuperanalysisSpringer Science & Business Media, 9 апр. 2013 г. - Всего страниц: 424 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. |
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2 | |
11 | |
References | 24 |
11 | 66 |
23 | 72 |
LINEAR ALGEBRA IN Z₂GRADED SPACES | 90 |
SUPERMANIFOLDS IN GENERAL | 131 |
LIE SUPERALGEBRAS | 170 |
LIE SUPERGROUPS | 245 |
LAPLACECASIMIR OPERATORS GEN | 279 |
OPERATORS ON THE LIE SUPERGROUUPS Up q | 312 |
CONSTRUCTION OF REPRESENTATIONS | 344 |
PARTICLE SPIN DYNAMICS AS | 374 |
SUPERSYMMETRY AND SUPERGRAVITY | 404 |
419 | |
LIE SUPERALGEBRAS | 231 |
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A₁ ad(x adjoint representation analogous analytic continuation anticommuting arbitrary automorphism B₁ basis Berezin called Cartan subalgebra coefficients commutator complex condition consider coordinates corresponding defined definition denote equation Əzi fibre follows formula G₁ Grassmann algebra Grassmann analytic Grassmann envelope h₁ Hamiltonian Hence homogeneous homomorphism infinitely differentiable integral invariant w.r.t. invertible involution isomorphism k₁ Laplace operator Lemma Lie algebra Lie group Lie superalgebra Lie supergroup linear space manifold mapping Mat(p matrix matrix elements morphism neighbourhood nondegenerate Note obtain odd elements parity automorphism phase space Poisson bracket polynomial presheaf Proof radial relation respect retraction right-hand side satisfies sdet Section sheaf spin subgroup subspace superdeterminant supergravity supermanifold supersymmetry symmetric system of canonical Theorem theory transformations U₁ usual variables vector Weyl group x₁ Y₁ Z₂-graded