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Singular Quadratic Forms in Perturbation Theory

  • Book
  • © 1999

Overview

Authors:
  1. Volodymyr Koshmanenko

    1. Institute of Mathematics, National Academy of Sciences, Kiev, Ukraine

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Part of the book series: Mathematics and Its Applications (MAIA, volume 474)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-viii
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  2. Introduction

    • Volodymyr Koshmanenko
    Pages 1-4

  3. Quadratic Forms and Linear Operators

    • Volodymyr Koshmanenko
    Pages 5-58

  4. Singular Quadratic Forms

    • Volodymyr Koshmanenko
    Pages 59-121

  5. Singular Perturbations of Self-Adjoint Operators

    • Volodymyr Koshmanenko
    Pages 123-225

  6. Applications to Quantum Field Theory

    • Volodymyr Koshmanenko
    Pages 227-279

  7. Back Matter

    Pages 281-312
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Keywords

About this book

The notion of singular quadratic form appears in mathematical physics as a tool for the investigation of formal expressions corresponding to perturbations devoid of operator sense. Numerous physical models are based on the use of Hamiltonians containing perturba­ tion terms with singular properties. Typical examples of such expressions are Schrodin­ ger operators with O-potentials (-~ + AD) and Hamiltonians in quantum field theory with perturbations given in terms of operators of creation and annihilation (P(

Reviews

` ...this text is a valuable contribution to the literature on the abstract aspects of singular perturbation theory.'
Mathematical Reviews, 2001a

Authors and Affiliations

  • Institute of Mathematics, National Academy of Sciences, Kiev, Ukraine

    Volodymyr Koshmanenko

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