Read Local Zeta Regularization And The Scalar Casimir Effect: A General Approach Based On Integral Kernels

Local Zeta Regularization And The Scalar Casimir Effect: A General Approach Based On Integral Kernels

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Description: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. General Zeta Regularization for a Scalar FieldThe Zeta Regularized Stress-Energy VEV in Terms of Integral KernelsTotal Energy and Forces on the BoundarySome Variations of the Previous Schemes A Massless Field on the SegmentA Massless Field Between Parallel HyperplanesA Massive Field Constrained by Perpendicular HyperplanesA Massless Field in a Three-Dimensional WedgeA Scalar Field with a Harmonic Background PotentialA Massless Field Inside a Rectangular Box The "Improved" Stress-Energy TensorOn the Regularity of Some Integral KernelsA Contour Integral Representation for Mellin TransformsSome Identities for the Dirichlet Kernel in a Slab ConfigurationDerivation of Some Results on Boundary ForcesAn Explicit Expression for the Renormalized Dirichlet Kernel of Half-Integer Order Graduate students and researchers including academics in theoretical physics. Quantum Field Theory;Zeta Regularization;Casimir Effect;Stress-Energy Key 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)Explicit computations are carried out for several configurations, applying in a uniform way the general algorithmsGive a more intuitive approach to the subject by implementing the regularization using canonical quantization in a Lorentzian frameworkWe have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Local Zeta Regularization And The Scalar Casimir Effect: A General Approach Based On Integral Kernels. To get started finding Local Zeta Regularization And The Scalar Casimir Effect: A General Approach Based On Integral Kernels, you are right to find our website which has a comprehensive collection of manuals listed.
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Description: 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. General Zeta Regularization for a Scalar FieldThe Zeta Regularized Stress-Energy VEV in Terms of Integral KernelsTotal Energy and Forces on the BoundarySome Variations of the Previous Schemes A Massless Field on the SegmentA Massless Field Between Parallel HyperplanesA Massive Field Constrained by Perpendicular HyperplanesA Massless Field in a Three-Dimensional WedgeA Scalar Field with a Harmonic Background PotentialA Massless Field Inside a Rectangular Box The "Improved" Stress-Energy TensorOn the Regularity of Some Integral KernelsA Contour Integral Representation for Mellin TransformsSome Identities for the Dirichlet Kernel in a Slab ConfigurationDerivation of Some Results on Boundary ForcesAn Explicit Expression for the Renormalized Dirichlet Kernel of Half-Integer Order Graduate students and researchers including academics in theoretical physics. Quantum Field Theory;Zeta Regularization;Casimir Effect;Stress-Energy Key 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)Explicit computations are carried out for several configurations, applying in a uniform way the general algorithmsGive a more intuitive approach to the subject by implementing the regularization using canonical quantization in a Lorentzian frameworkWe have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Local Zeta Regularization And The Scalar Casimir Effect: A General Approach Based On Integral Kernels. To get started finding Local Zeta Regularization And The Scalar Casimir Effect: A General Approach Based On Integral Kernels, you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

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Local Zeta Regularization And The Scalar Casimir Effect: A General Approach Based On Integral Kernels

Local Zeta Regularization And The Scalar Casimir Effect: A General Approach Based On Integral Kernels

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