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

"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...

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Bibliographic Details
Main Author: Fermi, Davide, 1988-
Other Authors: Pizzocchero, Livio
Format: Electronic Book
Language:English
Published: Singapore : World Scientific Publishing Co. Pte Ltd., ©2018
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100 1 |a Fermi, Davide,  |d 1988- 
245 1 0 |a Local zeta regularization and the scalar Casimir effect  |h [electronic resource] :  |b a general approach based on integral kernels /  |c Davide Fermi, Livio Pizzocchero 
260 |a Singapore :  |b World Scientific Publishing Co. Pte Ltd.,  |c ©2018 
300 |a 1 online resource (274 p.) :  |b ill. (some col.) 
504 |a Includes bibliographical references (p. 239-249) and index 
505 0 |a 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 
520 |a "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 
533 |a Electronic reproduction  |b Singapore :  |c World Scientific,  |d [2017] 
538 |a Mode of access: World Wide Web 
588 |a Description based on online resource; title from PDF title page (viewed October 12, 2017) 
596 |a 22 
650 0 |a Casimir effect 
650 0 |a Electronic books 
650 0 |a Functions, Zeta 
700 1 |a Pizzocchero, Livio 
776 0 8 |i Print version:  |a Fermi, Davide, 1988-  |t Local zeta regularization and the scalar Casimir effect : a general approach based on integral kernels  |d Singapore : World Scientific Publishing Co Pte Ltd., [2018]  |z 9789813224995  |w (DLC)2017034088 
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