Wave Equations on Lorentzian Manifolds and Quantization

Details Wave Equations on Lorentzian Manifolds and Quantization Wave Equations on Lorentzian Manifolds and Quantization

2008-06-05

arxiv.org/abs/0806.1036v1

ESI Lectures in Mathematics and Physics, European Mathematical Society Publishing House, ISBN 978-3-03719-037-1, March 2007, S

Mathematics

Differential Geometry

199 pages, 43 figures, order information for a hardcopy: http://www.ems-ph.org/order.php

Scientific paper

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.

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