Mathematics and Its Applications

Superanalysis

Authors: Khrennikov, Andrei Y.

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About this book

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.

Reviews

`The book will probably make a useful addition to the office|library collection of every researcher or mathematical centre with interests in analysis with anticommuting variables.'
Mathematical Reviews Clippings (2001)

Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-94-011-4609-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.99
price for USA in USD
  • ISBN 978-0-7923-5607-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.99
price for USA in USD
  • ISBN 978-94-010-5948-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Superanalysis
Authors
Series Title
Mathematics and Its Applications
Series Volume
470
Copyright
1999
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-011-4609-8
DOI
10.1007/978-94-011-4609-8
Hardcover ISBN
978-0-7923-5607-3
Softcover ISBN
978-94-010-5948-0
Edition Number
1
Number of Pages
IX, 357
Topics