Operators, Geometry and Quanta
Operators, Geometry and Quanta
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运算符、几何和量子
DOI：
10.1007/978-94-007-0205-9
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发表时间：
2011
影响因子：
5.4
通讯作者：
D. Vassilevich
中科院分区：
文献类型：
--
作者：
D. Fursaev;D. Vassilevich
本书对谱函数理论进行了详细且独立的介绍，重点是它们在量子场论中的应用。所有方法都通过当前研究前沿的特定物理问题的应用来说明，例如有限温度场理论、D-膜、量子孤子和非交换性。在本书的第一部分中，收集了有关微分几何和量子化的必要背景信息，包括不太标准的材料。本书的第二部分详细描述了主要谱函数及其计算方法。在第三部分中，该理论应用于几个例子（D-膜、量子孤子、反常现象、非交换性）。本书面向具有量子场论和微分几何基础知识的数学物理学高级研究生和研究人员。目的是让读者做好在自己的研究中使用光谱函数的准备，特别是与热核和 zeta 函数相关的光谱函数。
This book gives a detailed and self-contained introduction into the theory of spectral functions, with an emphasis on their applications to quantum field theory. All methods are illustrated with applications to specific physical problems from the forefront of current research, such as finite-temperature field theory, D-branes, quantum solitons and noncommutativity. In the first part of the book, necessary background information on differential geometry and quantization, including less standard material, is collected. The second part of the book contains a detailed description of main spectral functions and methods of their calculation. In the third part, the theory is applied to several examples (D-branes, quantum solitons, anomalies, noncommutativity). This book addresses advanced graduate students and researchers in mathematical physics with basic knowledge of quantum field theory and differential geometry. The aim is to prepare readers to use spectral functions in their own research, in particular in relation to heat kernels and zeta functions.