Superanalysis

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Superanalysis

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Author : Andrei Y. Khrennikov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Superanalysis written by Andrei Y. Khrennikov 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.

defined as elements of Grassmann algebra (an algebra with anticom muting generators). The derivatives of these elements with respect to anticommuting generators were defined according to algebraic laws, and nothing like Newton's analysis arose when Martin's approach was used. Later, during the next twenty years, the algebraic apparatus de veloped by Martin was used in all mathematical works. We must point out here the considerable contribution made by F. A. Berezin, G 1. Kac, D. A. Leites, B. Kostant. In their works, they constructed a new division of mathematics which can naturally be called an algebraic superanalysis. Following the example of physicists, researchers called the investigations carried out with the use of commuting and anticom muting coordinates supermathematics; all mathematical objects that appeared in supermathematics were called superobjects, although, of course, there is nothing "super" in supermathematics. However, despite the great achievements in algebraic superanaly sis, this formalism could not be regarded as a generalization to the case of commuting and anticommuting variables from the ordinary Newton analysis. What is more, Schwinger's formalism was still used in practically all physical works, on an intuitive level, and physicists regarded functions of anticommuting variables as "real functions" == maps of sets and not as elements of Grassmann algebras. In 1974, Salam and Strathdee proposed a very apt name for a set of super points. They called this set a superspace.

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.

Superanalysis

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Author : Andrei Y. Khrennikov
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-09-30

Superanalysis written by Andrei Y. Khrennikov 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 1999-09-30 with Mathematics categories.

defined as elements of Grassmann algebra (an algebra with anticom muting generators). The derivatives of these elements with respect to anticommuting generators were defined according to algebraic laws, and nothing like Newton's analysis arose when Martin's approach was used. Later, during the next twenty years, the algebraic apparatus de veloped by Martin was used in all mathematical works. We must point out here the considerable contribution made by F. A. Berezin, G 1. Kac, D. A. Leites, B. Kostant. In their works, they constructed a new division of mathematics which can naturally be called an algebraic superanalysis. Following the example of physicists, researchers called the investigations carried out with the use of commuting and anticom muting coordinates supermathematics; all mathematical objects that appeared in supermathematics were called superobjects, although, of course, there is nothing "super" in supermathematics. However, despite the great achievements in algebraic superanaly sis, this formalism could not be regarded as a generalization to the case of commuting and anticommuting variables from the ordinary Newton analysis. What is more, Schwinger's formalism was still used in practically all physical works, on an intuitive level, and physicists regarded functions of anticommuting variables as "real functions" == maps of sets and not as elements of Grassmann algebras. In 1974, Salam and Strathdee proposed a very apt name for a set of super points. They called this set a superspace.

Superanalysis

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Author : Andrei Y Khrennikov
language : en
Publisher:
Release Date : 1999-09-30

Superanalysis written by Andrei Y Khrennikov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-09-30 with categories.

P Adic Valued Distributions In Mathematical Physics

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Author : Andrei Y. Khrennikov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

P Adic Valued Distributions In Mathematical Physics written by Andrei Y. Khrennikov 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 2013-03-09 with Science categories.

Numbers ... , natural, rational, real, complex, p-adic .... What do you know about p-adic numbers? Probably, you have never used any p-adic (nonrational) number before now. I was in the same situation few years ago. p-adic numbers were considered as an exotic part of pure mathematics without any application. I have also used only real and complex numbers in my investigations in functional analysis and its applications to the quantum field theory and I was sure that these number fields can be a basis of every physical model generated by nature. But recently new models of the quantum physics were proposed on the basis of p-adic numbers field Qp. What are p-adic numbers, p-adic analysis, p-adic physics, p-adic probability? p-adic numbers were introduced by K. Hensel (1904) in connection with problems of the pure theory of numbers. The construction of Qp is very similar to the construction of (p is a fixed prime number, p = 2,3,5, ... ,127, ... ). Both these number fields are completions of the field of rational numbers Q. But another valuation 1 . Ip is introduced on Q instead of the usual real valuation 1 . I· We get an infinite sequence of non isomorphic completions of Q : Q2, Q3, ... , Q127, ... , IR = Qoo· These fields are the only possibilities to com plete Q according to the famous theorem of Ostrowsky.

Pseudo Differential Operators And Related Topics

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Author : Paolo Boggiatto
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-21

Pseudo Differential Operators And Related Topics written by Paolo Boggiatto 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 2006-03-21 with Mathematics categories.

Contains articles based on lectures given at the International Conference on Pseudo-differential Operators and Related Topics at Vaxjo University in Sweden from June 22 to June 25, 2005. Sixteen refereed articles cover a spectrum of topics such as partial differential equations, Wigner transforms, mathematical physics, and more.

Domain Specific Program Generation

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Author : Christian Lengauer
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-05-24

Domain Specific Program Generation written by Christian Lengauer 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 2004-05-24 with Computers categories.

Program generation holds the promise of helping to bridge the gap between application-level problem solutions and efficient implementations at the level of today's source programs as written in C or Java. Thus, program generation can substantially contribute to reducing production cost and time-to-market in future software production, while improving the quality and stability of the product. This book is about domain-specific program generation; it is the outcome of a Dagstuhl seminar on the topic held in March 2003. After an introductory preface by the volume editors, the 18 carefully reviewed revised full papers presented are organized into topical sections on - surveys of domain-specific programming technologies - domain-specific programming languages - tool support for program generation - domain-specific techniques for program optimization

Mathematics Of The Ussr

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Author :
language : en
Publisher:
Release Date : 1992

Mathematics Of The Ussr written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.

Theoretical And Mathematical Physics

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Author : Vasiliĭ Sergeevich Vladimirov
language : en
Publisher: American Mathematical Soc.
Release Date : 1988

Theoretical And Mathematical Physics written by Vasiliĭ Sergeevich Vladimirov 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 1988 with Mathematics categories.

Russian Mathematical Surveys

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Author :
language : en
Publisher:
Release Date : 1993

Russian Mathematical Surveys written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematicians categories.