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Perturbation of Spectra in Hilbert Space
K. O. Friedrichs
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Lectures in Applied Mathematics
1965; 178 pp; softcover
Volume: 3
ISBN-10: 0-8218-4682-5
ISBN-13: 978-0-8218-4682-7
List Price: US$43
Member Price: US$34.40
Order Code: LAM/3.S
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The mathematics of the quantum theory of fields has been a continuing puzzle to mathematicians and physicists for many decades. Perturbation theory remains an important element of quantum mechanics. Computationally, it is one of the most successful methods available. However, various features of field theory produce difficulties with the perturbative approach. Here, Friedrichs assumes certain smoothness of the interaction Hamiltonian, which eliminates divergence of the terms in the perturbation expansion, but, as a consequence, forces him to give up the possibility of a local Lorentz-invariant interaction.

In this book based on his 1960 lectures in Boulder, Friedrichs looks at some of the unresolved mathematical questions in the quantum field theory of the time, with an emphasis on problems coming from perturbation theory. The lectures begin with an introduction to perturbation theory of discrete and continuous spectra and the theory of scattering. These methods are then applied to perturbations by annihilation and creation operators. Each of the three chapters has a corresponding appendix, where Friedrichs discusses some alternative approaches and additional material relating to the main text.

Readership

Graduate students and research mathematicians interested in analysis.

Table of Contents

  • I. The perturbation problem. Perturbation of discrete spectra
  • II. Peturbations of operators having continuous spectra
  • III. Perturbation by annihilation-creation operators
  • Appendix to chapter 1
  • Appendix to chapter II
  • Appendix to chapter III
  • Bibliography to chapter I
  • Bibliography to chapter II
  • Bibliography to chapter III
  • Author index
  • Subject index
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