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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 978-3-03719-537-6DOI 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
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