Wave Equations on Lorentzian Manifolds and Quantization
Wave Equations on Lorentzian Manifolds and Quantization
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DOI：
10.4171/037
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发表时间：
2007-03
期刊：
影响因子：
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通讯作者：
Christian Baer;N. Ginoux;Frank Pfaeffle
中科院分区：
文献类型：
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作者：
Christian Baer;N. Ginoux;Frank Pfaeffle
本书详细介绍了洛伦兹流形上的线性波动方程（用于矢量束值场）。在第一章收集了初步材料之后，我们在第二章找到了局部基本解的构建及其Hadamard扩展。第三章建立了全局双曲时空上全局基本解的存在唯一性，讨论了柯西问题的格林算子和适定性。最后一章致力于在代数量子场论的意义上的场量子化。对C*代数和ccr表示的必要基础进行了详细的开发。文本提供了一个独立的介绍，这些主题的研究生在数学和物理。同时，它的目的是作为研究人员在全局分析，广义相对论和量子场论的参考。
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.