Wave Equations on Lorentzian Manifolds and Quantization
By Christian Baer, Nicolas Ginoux, Frank Pfaeffle. 2007
477 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/a8cdf65c1995bf314a89dfc1d2c848877fedd401
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In Applied Mathematics
Citations in the corpus
- Maximally homogeneous para-CR manifolds of semisimple type (2006, unknown): “uations contain the relevant results for small domains in Lorentzian manifolds or for very special manifolds such as Minkowski space. In this text we summarize the global analytic results obtained in [4], see also Leray’s unpublished lecture notes [13] and Choquet-Bruhat’s exposition [7]. In order t”
- Algebraic QFT in Curved Spacetime and Quasifree Hadamard States: An Introduction (2014, background): “Everything is a consequence of the fact that M is globally hyperbolic [2] .”