# Wave Equations on Lorentzian Manifolds and Quantization

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*Christian Bär; Nicolas Ginoux; Frank Pfäffle*

A publication of the European Mathematical Society

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.