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Wave Equations on Lorentzian Manifolds and Quantization
ESI Lectures in Mathematics and Physics

Christian Bär (University of Potsdam, Germany)
Nicolas Ginoux (University of Regensburg, Germany)
Frank Pfäffle (University of Potsdam, Germany)

Wave Equations on Lorentzian Manifolds and Quantization

ISBN print 978-3-03719-037-1, ISBN online 978-3-03719-537-6
DOI 10.4171/037
March 2007, 202 pages, softcover, 17 x 24 cm.
38.00 Euro

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.

Further Information

Review in Zentralblatt MATH 1118.58016

Review in MR 2298021 (2008j:58041)

EMS Review