TY  - BOOK
AU  - Bär,Christian
AU  - Bär,Christian
AU  - Ginoux,Nicolas
AU  - Pfäffle,Frank
TI  - Wave Equations on Lorentzian Manifolds and Quantization
T2  - ESI Lectures in Mathematics and Physics (ESI)
SN  - 9783037195376
PY  - 2007///
CY  - Zuerich, Switzerland
PB  - European Mathematical Society Publishing House
KW  - Differential & Riemannian geometry
KW  - bicssc
KW  - Differential equations
KW  - Global analysis, analysis on manifolds
KW  - msc
KW  - Partial differential equations
KW  - Differential geometry
N1  - Restricted to subscribers
N2  - 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
UR  - https://doi.org/10.4171/037
UR  - http://www.ems-ph.org/img/books/baer_mini.jpg
ER  -