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# ðŸ“™ Wave Equations on Lorentzian Manifolds and Quantization (Esi Lectures in Mathematics and Physics) by Christian Bar, Nicolas Ginoux, Frank Pfaffle â€” epub download

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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.

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- Author:
**Christian Bar, Nicolas Ginoux, Frank Pfaffle** - Year:
**2007** - Publisher:
**American Mathematical Society** - Language:
**English** - ISBN:
**303719037X,9783037190371**

- File size:
**2 235 633** - Format:
**pdf**

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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 funda...

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 funda...

The purpose of this handbook is to give an overview of some recent developments in differential geometry related to supersymmetric field theories. The main themes covered are: Special geometry and supersymmetry Generalized geometry Geometries with ...

The purpose of this handbook is to give an overview of some recent developments in differential geometry related to supersymmetric field theories. The main themes covered are: Special geometry and supersymmetry Generalized geometry Geometries with ...

This manuscript is a detailed presentation of the ten lectures given by the author at the NSF Regional Conference on Three-Manifold Topology, held October 1977, at Virginia Polytechnic Institute and State University. The purpose of the conference was to p...

This work presents three types of problems in the theory of nonlinear wave equations that have varying degrees of non-trivial overlap with harmonic analysis. The author discusses results including existence for certain quasilinear wave equations and for s...

Differential geometry techniques have very useful and important applications in partial differential equations and quantum mechanics. This work presents a purely geometric treatment of problems in physics involving quantum harmonic oscillators, quartic os...

This manuscript is a detailed presentation of the ten lectures given by the author at the NSF Regional Conference on Three-Manifold Topology, held October 1977, at Virginia Polytechnic Institute and State University. The purpose of the conference was to p...

This manuscript is a detailed presentation of the ten lectures given by the author at the NSF Regional Conference on Three-Manifold Topology, held October 1977, at Virginia Polytechnic Institute and State University. The purpose of the conference was to p...