Ten Physical Applications Of Spectral Zeta Functions

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Ten Physical Applications Of Spectral Zeta Functions

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Author : Emilio Elizalde
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-04

Ten Physical Applications Of Spectral Zeta Functions written by Emilio Elizalde and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-04 with Science categories.

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).

A Window Into Zeta And Modular Physics

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Author : Klaus Kirsten
language : en
Publisher: Cambridge University Press
Release Date : 2010-05-24

A Window Into Zeta And Modular Physics written by Klaus Kirsten and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-24 with Mathematics categories.

Consists of lectures that are part of the MSRI workshops and that introduce students and researchers to the intriguing world of theoretical physics.

Cosmology Quantum Vacuum And Zeta Functions

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Author : Sergey D. Odintsov
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-10

Cosmology Quantum Vacuum And Zeta Functions written by Sergey D. Odintsov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-10 with Science categories.

Some major developments of physics in the last three decades are addressed by highly qualified specialists in different specific fields. They include renormalization problems in QFT, vacuum energy fluctuations and the Casimir effect in different configurations, and a wealth of applications. A number of closely related issues are also considered. The cosmological applications of these theories play a crucial role and are at the very heart of the book; in particular, the possibility to explain in a unified way the whole history of the evolution of the Universe: from primordial inflation to the present day accelerated expansion. Further, a description of the mathematical background underlying many of the physical theories considered above is provided. This includes the uses of zeta functions in physics, as in the regularization problems in QFT already mentioned, specifically in curved space-time, and in Casimir problems as.

Zeta And Q Zeta Functions And Associated Series And Integrals

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Author : Hari M Srivastava
language : en
Publisher: Elsevier
Release Date : 2011-10-11

Zeta And Q Zeta Functions And Associated Series And Integrals written by Hari M Srivastava and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-11 with Mathematics categories.

Zeta and q-Zeta Functions and Associated Series and Integrals is a thoroughly revised, enlarged and updated version of Series Associated with the Zeta and Related Functions. Many of the chapters and sections of the book have been significantly modified or rewritten, and a new chapter on the theory and applications of the basic (or q-) extensions of various special functions is included. This book will be invaluable because it covers not only detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions, but stimulating historical accounts of a large number of problems and well-classified tables of series and integrals. - Detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions

Quantum Field Theory I Basics In Mathematics And Physics

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Author : Eberhard Zeidler
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-18

Quantum Field Theory I Basics In Mathematics And Physics written by Eberhard Zeidler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-18 with Science categories.

This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists, at levels ranging from advanced undergraduate students to professional scientists. The book bridges the acknowledged gap between the different languages used by mathematicians and physicists. For students of mathematics the author shows that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which goes beyond the usual curriculum in physics.

Sturm Liouville Operators Their Spectral Theory And Some Applications

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Author : Fritz Gesztesy
language : en
Publisher: American Mathematical Society
Release Date : 2024-09-24

Sturm Liouville Operators Their Spectral Theory And Some Applications written by Fritz Gesztesy and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-24 with Mathematics categories.

This book provides a detailed treatment of the various facets of modern Sturm?Liouville theory, including such topics as Weyl?Titchmarsh theory, classical, renormalized, and perturbative oscillation theory, boundary data maps, traces and determinants for Sturm?Liouville operators, strongly singular Sturm?Liouville differential operators, generalized boundary values, and Sturm?Liouville operators with distributional coefficients. To illustrate the theory, the book develops an array of examples from Floquet theory to short-range scattering theory, higher-order KdV trace relations, elliptic and algebro-geometric finite gap potentials, reflectionless potentials and the Sodin?Yuditskii class, as well as a detailed collection of singular examples, such as the Bessel, generalized Bessel, and Jacobi operators. A set of appendices contains background on the basics of linear operators and spectral theory in Hilbert spaces, Schatten?von Neumann classes of compact operators, self-adjoint extensions of symmetric operators, including the Friedrichs and Krein?von Neumann extensions, boundary triplets for ODEs, Krein-type resolvent formulas, sesquilinear forms, Nevanlinna?Herglotz functions, and Bessel functions.

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

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Author : Davide Fermi
language : en
Publisher: World Scientific
Release Date : 2017-10-06

Local Zeta Regularization And The Scalar Casimir Effect A General Approach Based On Integral Kernels written by Davide Fermi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-06 with Science categories.

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.

African Americans In Mathematics

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Author : Nathaniel Dean
language : en
Publisher: American Mathematical Soc.
Release Date : 1997

African Americans In Mathematics written by Nathaniel Dean and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.

This volume contains contains research and expository papers by African-American mathematicians on issues related to their involvement in the mathematical sciences. Little is known, taught, or written about African-American mathematicians. Information is lacking on their past and present contributions and on the qualitive nature of their existence in and distribution throughout mathematics. This lack of information leads to a number of questions that have to date remainedunanswered. This volume provides details and pointers to help answer some of these questions.

Complex Numbers

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Author : S C Roy
language : en
Publisher: Elsevier
Release Date : 2007-07-01

Complex Numbers written by S C Roy and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-01 with Mathematics categories.

An informative and useful account of complex numbers that includes historical anecdotes, ideas for further research, outlines of theory and a detailed analysis of the ever-elusory Riemann hypothesis. Stephen Roy assumes no detailed mathematical knowledge on the part of the reader and provides a fascinating description of the use of this fundamental idea within the two subject areas of lattice simulation and number theory. Complex Numbers offers a fresh and critical approach to research-based implementation of the mathematical concept of imaginary numbers. Detailed coverage includes: - Riemann's zeta function: an investigation of the non-trivial roots by Euler-Maclaurin summation. - Basic theory: logarithms, indices, arithmetic and integration procedures are described. - Lattice simulation: the role of complex numbers in Paul Ewald's important work of the I 920s is analysed. - Mangoldt's study of the xi function: close attention is given to the derivation of N(T) formulae by contour integration. - Analytical calculations: used extensively to illustrate important theoretical aspects. - Glossary: over 80 terms included in the text are defined. - Offers a fresh and critical approach to the research-based implication of complex numbers - Includes historical anecdotes, ideas for further research, outlines of theory and a detailed analysis of the Riemann hypothesis - Bridges any gaps that might exist between the two worlds of lattice sums and number theory

From Fields To Strings Circumnavigating Theoretical Physics Ian Kogan Memorial Collection In 3 Vols

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Author : Shifman Misha
language : en
Publisher: World Scientific
Release Date : 2005-02-03

From Fields To Strings Circumnavigating Theoretical Physics Ian Kogan Memorial Collection In 3 Vols written by Shifman Misha and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-03 with Science categories.

This volume is a collection of dedicated reviews covering all aspects of theoretical high energy physics and some aspects of solid state physics. Some of the papers are broad reviews of topics that span the entire field while others are surveys of authors' personal achievements. This is the most comprehensive review collection reflecting state of the art at the end of 2004. An important and unique aspect is a special effort the authors have invested in making the presentation pedagogical.