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Bose Algebras: The Complex and Real Wave Representations

  • Authors
  • Torben T. Nielsen

Part of the Lecture Notes in Mathematics book series (LNM, volume 1472)

Table of contents

  1. Front Matter
    Pages I-V
  2. Torben T. Nielsen
    Pages 1-3
  3. Torben T. Nielsen
    Pages 4-22
  4. Torben T. Nielsen
    Pages 23-32
  5. Torben T. Nielsen
    Pages 33-44
  6. Torben T. Nielsen
    Pages 45-52
  7. Torben T. Nielsen
    Pages 53-65
  8. Torben T. Nielsen
    Pages 66-71
  9. Torben T. Nielsen
    Pages 72-78
  10. Torben T. Nielsen
    Pages 79-88
  11. Torben T. Nielsen
    Pages 89-93
  12. Back Matter
    Pages 94-132

About this book

Introduction

The mathematics of Bose-Fock spaces is built on the notion of a commutative algebra and this algebraic structure makes the theory appealing both to mathematicians with no background in physics and to theorectical and mathematical physicists who will at once recognize that the familiar set-up does not obscure the direct relevance to theoretical physics. The well-known complex and real wave representations appear here as natural consequences of the basic mathematical structure - a mathematician familiar with category theory will regard these representations as functors. Operators generated by creations and annihilations in a given Bose algebra are shown to give rise to a new Bose algebra of operators yielding the Weyl calculus of pseudo-differential operators. The book will be useful to mathematicians interested in analysis in infinitely many dimensions or in the mathematics of quantum fields and to theoretical physicists who can profit from the use of an effective and rigrous Bose formalism.

Keywords

Algebraic structure Category theory Theoretical physics algebra calculus commutative algebra

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0098303
  • Copyright Information Springer-Verlag Berlin Heidelberg 1991
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-54041-0
  • Online ISBN 978-3-540-47367-1
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site