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Local zeta regularization and the scalar Casimir effect : a general approach based on integral kernels

Author: Davide Fermi; Livio Pizzocchero
Publisher: Singapore ; Hackensack, NJ : World Scientific Publishing Co. Pte. Ltd., [2018] ©2018
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
"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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Fermi, Davide, 1988-
Local zeta regularization and the scalar Casimir effect.
Singapore ; Hackensack, NJ : World Scientific Publishing Co. Pte. Ltd., [2018]
(DLC) 2017034088
(OCoLC)990571129
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Davide Fermi; Livio Pizzocchero
ISBN: 9789813225008 9813225009 9789813225015 9813225017
OCLC Number: 1008987210
Description: 1 online resource (xviii, 255 pages).
Contents: Zeta regularization for a scalar field --
The zeta regularized stress-energy VEV in terms of integral kernels --
Total energy and forces on the boundary --
Some variations of the previous schemes --
A massless field on the segment --
A massless field between parallel hyperplanes --
A massive field constrained by perpendicular hyperplanes --
A massless field in a three-dimensional wedge --
A scalar field with a harmonic background potential --
A massless field inside a rectangular box.
Responsibility: Davide Fermi, Livio Pizzocchero.

Abstract:

"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."--Publisher's website.

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