LOCAL ZETA REGULARIZATION AND THE SCALAR CASIMIR EFFECT:A GENERAL APPROACH BASED ON INTEGRAL KERNELS

局部Zeta规则化与标量卡西米尔效应:以积分核为基础的通用方法

工业工程学

原   价:
998.75
售   价:
799.00
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平台大促 低至8折优惠
发货周期:预计3-5周发货
出  版 社
出版时间
2017年11月09日
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ISBN
9789813224995
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页      码
200
语      种
英文
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图书简介
Zeta regularization is a method to treat the divergent quantities appearing in several areas of mathematical physics and, in particular, in quantum field theory; it is based on the fascinating idea that a finite value can be ascribed to a formally divergent expression via analytic continuation with respect to a complex regulating parameter. This book provides a thorough overview of zeta regularization for the vacuum expectation values of the most relevant observables of a quantized, neutral scalar field in Minkowski spacetime; the field can be confined to a spatial domain, with suitable boundary conditions, and an external potential is possibly present. Zeta regularization is performed in this framework for both local and global observables, like the stress-energy tensor and the total energy; the analysis of their vacuum expectation values accounts for the Casimir physics of the system. The analytic continuation process required in this setting by zeta regularization is deeply linked to some integral kernels; these are determined by the fundamental elliptic operator appearing in the evolution equation for the quantum field. The book provides a systematic illustration of these connections, devised as a toolbox for explicit computations in specific configurations; many examples are presented. A comprehensive account is given of the existing literature on this subject, including the previous work of the authors. The book will be useful to anyone interested in a mathematically sound description of quantum vacuum effects, from graduate students to scientists working in this area. Key Features: o Zeta regularization is used in a systematic way for both local and global aspects related to the vacuum state of a quantized field, marking a difference with respect to the existing literature, in which local aspects (say, the stress-energy tensor) do not receive the full attention they would deserve (especially, in the presence of boundary conditions) o Explicit computations are carried out for several configurations, applying in a uniform way the general algorithms o Give a more intuitive approach to the subject by implementing the regularization using canonical quantization in a Lorentzian framework
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