01860nam a2200217Ia 4500 CTU_134133 210402s9999 xx 000 0 und d 1754000 530.12 B223 Bar, Christian Wave equations on Lorentzian manifolds and quantization Christian Bär, Nicolas Ginoux and Frank Pfäffle Zürich, Switzerland European Mathematical Society 2007 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 ^* 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. Wave equation,Geometry, Differential,Complex manifolds,Geometric quantization,Cauchy problem,Phương trình sóng Numerical solutions,Hình học, Vi phân Nguyễn Kim Chung Trung tâm Học liệu Trường Đại học Cần Thơ