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Wave Equations on Lorentzian Manifolds and Quantization
Christian Bär, Nicolas Ginoux, and Frank Pfäffle, University of Potsdam, Germany
A publication of the European Mathematical Society.
cover
ESI Lectures in Mathematics and Physics
2007; 202 pp; softcover
Volume: 3
ISBN-10: 3-03719-037-X
ISBN-13: 978-3-03719-037-1
List Price: US$44
Member Price: US$35.20
Order Code: EMSESILEC/3
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This book provides a detailed introduction to linear wave equations on Lorentzian manifolds (for vector-bundle valued fields). After a collection of preliminary material in the first chapter, one finds in the second chapter the construction of local fundamental solutions together with their Hadamard expansion. The third chapter establishes the existence and uniqueness of global fundamental solutions on globally hyperbolic spacetimes and discusses Green's operators and well-posedness of the Cauchy problem. The last chapter is devoted to field quantization in the sense of algebraic quantum field theory. The necessary basics on \(C^*\)-algebras and CCR-representations are developed in full detail.

The text provides a self-contained introduction to these topics addressed to graduate students in mathematics and physics. At the same time, it is intended as a reference for researchers in global analysis, general relativity, and quantum field theory.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

Readership

Graduate students and research mathematicians interested in mathematical physics.

Table of Contents

  • Preliminaries
  • The local theory
  • The global theory
  • Quantization
  • Appendix. Background material
  • Bibliography
  • Figures
  • Symbols
  • Index
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