Local Zeta Regularization And The Scalar Casimir Effect: A General Approach Based On Integral Kernels PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Local Zeta Regularization And The Scalar Casimir Effect: A General Approach Based On Integral Kernels PDF full book. Access full book title Local Zeta Regularization And The Scalar Casimir Effect: A General Approach Based On Integral Kernels by Davide Fermi. Download full books in PDF and EPUB format.
Author: Davide Fermi
Publisher: World Scientific
ISBN: 9813225017
Category : Science
Languages : en
Pages : 274
Get Book Here
Book 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.
Author: Davide Fermi
Publisher: World Scientific
ISBN: 9813225017
Category : Science
Languages : en
Pages : 274
Get Book Here
Book 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.
Author: Alessandro Michelangeli
Publisher: Springer
ISBN: 3319589040
Category : Mathematics
Languages : en
Pages : 292
Get Book Here
Book Description
This volume collects recent contributions on the contemporary trends in the mathematics of quantum mechanics, and more specifically in mathematical problems arising in quantum many-body dynamics, quantum graph theory, cold atoms, unitary gases, with particular emphasis on the developments of the specific mathematical tools needed, including: linear and non-linear Schrödinger equations, topological invariants, non-commutative geometry, resonances and operator extension theory, among others. Most of contributors are international leading experts or respected young researchers in mathematical physics, PDE, and operator theory. All their material is the fruit of recent studies that have already become a reference in the community. Offering a unified perspective of the mathematics of quantum mechanics, it is a valuable resource for researchers in the field.
Author: Andrei A Bytsenko
Publisher: World Scientific
ISBN: 9814502987
Category : Science
Languages : en
Pages : 336
Get Book Here
Book Description
This book is the result of several years of work by the authors on different aspects of zeta functions and related topics. The aim is twofold. On one hand, a considerable number of useful formulas, essential for dealing with the different aspects of zeta-function regularization (analytic continuation, asymptotic expansions), many of which appear here, in book format, for the first time are presented. On the other hand, the authors show explicitly how to make use of such formulas and techniques in practical applications to physical problems of very different nature. Virtually all types of zeta functions are dealt with in the book.
Author: Michael Bordag
Publisher: International Monographs on Ph
ISBN: 019923874X
Category : Science
Languages : en
Pages : 768
Get Book Here
Book Description
This book is a comprehensive sourcebook, distilled from hundreds of recently published papers, about the Casimir effect: the small forces originating from the quantum vacuum and acting between closely spaced bodies. It brings together developments in experiment and theory, fundamental and applied aspects of the Casimir force.
Author: Michele Correggi
Publisher: Springer Nature
ISBN: 9819958849
Category : Science
Languages : en
Pages : 371
Get Book Here
Book Description
This book is the second volume that provides an unique overview of the most recent and relevant contributions in the field of mathematical physics with a focus on the mathematical features of quantum mechanics. It is a collection of review papers together with brand new works related to the activities of the INdAM Intensive Period "INdAM Quantum Meetings (IQM22)", which took place at the Politecnico di Milano in Spring 2022 at Politecnico di Milano. The range of topics covered by the book is wide, going ranging from many-body quantum mechanics to quantum field theory and open quantum systems.
Author: Sergio Albeverio
Publisher: Springer Science & Business Media
ISBN: 3642882013
Category : Science
Languages : en
Pages : 458
Get Book Here
Book Description
Next to the harmonic oscillator and the Coulomb potential the class of two-body models with point interactions is the only one where complete solutions are available. All mathematical and physical quantities can be calculated explicitly which makes this field of research important also for more complicated and realistic models in quantum mechanics. The detailed results allow their implementation in numerical codes to analyse properties of alloys, impurities, crystals and other features in solid state quantum physics. This monograph presents in a systematic way the mathematical approach and unifies results obtained in recent years. The student with a sound background in mathematics will get a deeper understanding of Schrödinger Operators and will see many examples which may eventually be used with profit in courses on quantum mechanics and solid state physics. The book has textbook potential in mathematical physics and is suitable for additional reading in various fields of theoretical quantum physics.
Author: Emilio Elizalde
Publisher: Springer Science & Business Media
ISBN: 3540447571
Category : Science
Languages : en
Pages : 229
Get Book Here
Book Description
This monography is, in the first place, a commented guide that invites the reader to plunge into the thrilling world ofzeta functions and their appli cations in physics. Different aspects ofthis field ofknowledge are considered, as one can see specifically in the Table of Contents. The level of the book is elementary. It is intended for people with no or little knowledge of the subject. Everything is explained in full detail, in particular, the mathematical difficulties and tricky points, which too often constitute an insurmountable barrier for those who would have liked to be come aquainted with that matter but never dared to ask (or did not manage to understand more complete, higher-level treatises). In this sense the present work is to be considered as a basic introduction and exercise collection for other books that have appeared recently. Concerning the physical applications of the method ofzeta-function reg ularization here described, quite a big choice is presented. The reader must be warned, however, that I have not tried to explain the underlying physi cal theories in complete detail (since this is undoubtedly out of scope), but rather to illustrate - simply and clearly - the precise way the method must be applied. Sometimes zeta regularization is explicitly compared in the text with other procedures the reader is supposed to be more familiar with (such as cut-off or dimensional regularization).
Author: Andreas Wipf
Publisher: Springer Nature
ISBN: 3030832635
Category : Science
Languages : en
Pages : 568
Get Book Here
Book Description
This new expanded second edition has been totally revised and corrected. The reader finds two complete new chapters. One covers the exact solution of the finite temperature Schwinger model with periodic boundary conditions. This simple model supports instanton solutions – similarly as QCD – and allows for a detailed discussion of topological sectors in gauge theories, the anomaly-induced breaking of chiral symmetry and the intriguing role of fermionic zero modes. The other new chapter is devoted to interacting fermions at finite fermion density and finite temperature. Such low-dimensional models are used to describe long-energy properties of Dirac-type materials in condensed matter physics. The large-N solutions of the Gross-Neveu, Nambu-Jona-Lasinio and Thirring models are presented in great detail, where N denotes the number of fermion flavors. Towards the end of the book corrections to the large-N solution and simulation results of a finite number of fermion flavors are presented. Further problems are added at the end of each chapter in order to guide the reader to a deeper understanding of the presented topics. This book is meant for advanced students and young researchers who want to acquire the necessary tools and experience to produce research results in the statistical approach to Quantum Field Theory.
Author:
Publisher:
ISBN:
Category : Power resources
Languages : en
Pages : 1010
Get Book Here
Book Description
Author: Bei-Lok B. Hu
Publisher: Cambridge University Press
ISBN: 0521193575
Category : Science
Languages : en
Pages : 615
Get Book Here
Book Description
An overview of semi-classical gravity theory and stochastic gravity as theories of quantum gravity in curved space-time.
