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Bose Algebras: The Complex and Real Wave Representations

  • Book
  • © 1991

Overview

Authors:
  1. Torben T. Nielsen
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1472)

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-V
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  2. Introduction

    • Torben T. Nielsen
    Pages 1-3

  3. The Bose algebra Γ0ℌ,〈,〉

    • Torben T. Nielsen
    Pages 4-22

  4. Lifting operators to Γℋ

    • Torben T. Nielsen
    Pages 23-32

  5. The coherent vectors in Γℋ

    • Torben T. Nielsen
    Pages 33-44

  6. The Wick ordering and the Weyl relations

    • Torben T. Nielsen
    Pages 45-52

  7. Some special operators

    • Torben T. Nielsen
    Pages 53-65

  8. The complex wave representation

    • Torben T. Nielsen
    Pages 66-71

  9. The real wave representation

    • Torben T. Nielsen
    Pages 72-78

  10. Bose algebras of operators

    • Torben T. Nielsen
    Pages 79-88

  11. Wave representations of Γ(ℋ+ℋ*)

    • Torben T. Nielsen
    Pages 89-93

  12. Back Matter

    Pages 94-132
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Bose Algebras: The Complex and Real Wave Representations

  • Authors: Torben T. Nielsen

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0098303

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1991

  • Softcover ISBN: 978-3-540-54041-0Published: 19 June 1991

  • eBook ISBN: 978-3-540-47367-1Published: 08 December 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VI, 138

  • Topics: Analysis, Theoretical, Mathematical and Computational Physics

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