Zeta Regularization Techniques With Applications

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Zeta Regularization Techniques with Applications

Author : E. Elizalde
Publisher : World Scientific
ISBN 13 : 9789810214418
Total Pages : 344 pages
Book Rating : 4.2/5 (144 download)

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Book Synopsis Zeta Regularization Techniques with Applications by : E. Elizalde

Download or read book Zeta Regularization Techniques with Applications written by E. Elizalde and published by World Scientific. This book was released on 1994 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Zeta Regularization Techniques With Applications

Author : Andrei A Bytsenko
Publisher : World Scientific
ISBN 13 : 9814502987
Total Pages : 336 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Zeta Regularization Techniques With Applications by : Andrei A Bytsenko

Download or read book Zeta Regularization Techniques With Applications written by Andrei A Bytsenko and published by World Scientific. This book was released on 1994-05-16 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Ten Physical Applications of Spectral Zeta Functions

Author : Emilio Elizalde
Publisher : Springer
ISBN 13 : 3642294057
Total Pages : 234 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Ten Physical Applications of Spectral Zeta Functions by : Emilio Elizalde

Download or read book Ten Physical Applications of Spectral Zeta Functions written by Emilio Elizalde and published by Springer. This book was released on 2012-05-31 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Zeta-function regularization is a powerful method in perturbation theory, and this book is a comprehensive guide for the student of this subject. Everything is explained in detail, in particular the mathematical difficulties and tricky points, and several applications are given to show how the procedure works in practice, for example in the Casimir effect, gravity and string theory, high-temperature phase transition, topological symmetry breaking, and non-commutative spacetime. The formulae, some of which are new, can be directly applied in creating physically meaningful, accurate numerical calculations. The book acts both as a basic introduction and a collection of exercises for those who want to apply this regularization procedure in practice. Thoroughly revised, updated and expanded, this new edition includes novel, explicit formulas on the general quadratic, the Chowla-Selberg series case, an interplay with the Hadamard calculus, and also features a fresh chapter on recent cosmological applications, including the calculation of the vacuum energy fluctuations at large scale in braneworld and other models.

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

Author : Davide Fermi
Publisher : World Scientific
ISBN 13 : 9813225017
Total Pages : 274 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Local Zeta Regularization And The Scalar Casimir Effect: A General Approach Based On Integral Kernels by : Davide Fermi

Download or read book Local Zeta Regularization And The Scalar Casimir Effect: A General Approach Based On Integral Kernels written by Davide Fermi and published by World Scientific. This book was released on 2017-10-06 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Window Into Zeta and Modular Physics

Author : Klaus Kirsten
Publisher : Cambridge University Press
ISBN 13 : 0521199301
Total Pages : 361 pages
Book Rating : 4.5/5 (211 download)

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Book Synopsis A Window Into Zeta and Modular Physics by : Klaus Kirsten

Download or read book A Window Into Zeta and Modular Physics written by Klaus Kirsten and published by Cambridge University Press. This book was released on 2010-05-24 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Consists of lectures that are part of the MSRI workshops and that introduce students and researchers to the intriguing world of theoretical physics.

Encyclopaedia of Mathematics, Supplement III

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
ISBN 13 : 0306483734
Total Pages : 564 pages
Book Rating : 4.3/5 (64 download)

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Book Synopsis Encyclopaedia of Mathematics, Supplement III by : Michiel Hazewinkel

Download or read book Encyclopaedia of Mathematics, Supplement III written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2007-11-23 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third supplementary volume to Kluwer's highly acclaimed twelve-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.

Cosmology, Quantum Vacuum and Zeta Functions

Author : Sergey D. Odintsov
Publisher : Springer Science & Business Media
ISBN 13 : 3642197604
Total Pages : 379 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Cosmology, Quantum Vacuum and Zeta Functions by : Sergey D. Odintsov

Download or read book Cosmology, Quantum Vacuum and Zeta Functions written by Sergey D. Odintsov and published by Springer Science & Business Media. This book was released on 2011-06-10 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Some Musings on Theta, Eta, and Zeta

Author : Floyd L. Williams
Publisher : Springer Nature
ISBN 13 : 9819953367
Total Pages : 233 pages
Book Rating : 4.8/5 (199 download)

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Book Synopsis Some Musings on Theta, Eta, and Zeta by : Floyd L. Williams

Download or read book Some Musings on Theta, Eta, and Zeta written by Floyd L. Williams and published by Springer Nature. This book was released on with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Zeta Functions over Zeros of Zeta Functions

Author : André Voros
Publisher : Springer Science & Business Media
ISBN 13 : 3642052037
Total Pages : 171 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Zeta Functions over Zeros of Zeta Functions by : André Voros

Download or read book Zeta Functions over Zeros of Zeta Functions written by André Voros and published by Springer Science & Business Media. This book was released on 2009-11-21 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this text, the famous zeros of the Riemann zeta function and its generalizations (L-functions, Dedekind and Selberg zeta functions)are analyzed through several zeta functions built over those zeros.

Advances in Quantum Mechanics

Author : Alessandro Michelangeli
Publisher : Springer
ISBN 13 : 3319589040
Total Pages : 292 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Advances in Quantum Mechanics by : Alessandro Michelangeli

Download or read book Advances in Quantum Mechanics written by Alessandro Michelangeli and published by Springer. This book was released on 2017-08-01 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Sturm?Liouville Operators, Their Spectral Theory, and Some Applications

Author : Fritz Gesztesy
Publisher : American Mathematical Society
ISBN 13 : 1470476665
Total Pages : 946 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Sturm?Liouville Operators, Their Spectral Theory, and Some Applications by : Fritz Gesztesy

Download or read book Sturm?Liouville Operators, Their Spectral Theory, and Some Applications written by Fritz Gesztesy and published by American Mathematical Society. This book was released on 2024-09-24 with total page 946 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Numerical Analysis or Numerical Method in Symmetry

Author : Clemente Cesarano
Publisher : MDPI
ISBN 13 : 3039283723
Total Pages : 194 pages
Book Rating : 4.0/5 (392 download)

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Book Synopsis Numerical Analysis or Numerical Method in Symmetry by : Clemente Cesarano

Download or read book Numerical Analysis or Numerical Method in Symmetry written by Clemente Cesarano and published by MDPI. This book was released on 2020-02-21 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Special Issue focuses mainly on techniques and the relative formalism typical of numerical methods and therefore of numerical analysis, more generally. These fields of study of mathematics represent an important field of investigation both in the field of applied mathematics and even more exquisitely in the pure research of the theory of approximation and the study of polynomial relations as well as in the analysis of the solutions of the differential equations both ordinary and partial derivatives. Therefore, a substantial part of research on the topic of numerical analysis cannot exclude the fundamental role played by approximation theory and some of the tools used to develop this research. In this Special Issue, we want to draw attention to the mathematical methods used in numerical analysis, such as special functions, orthogonal polynomials, and their theoretical tools, such as Lie algebra, to study the concepts and properties of some special and advanced methods, which are useful in the description of solutions of linear and nonlinear differential equations. A further field of investigation is dedicated to the theory and related properties of fractional calculus with its adequate application to numerical methods.

African Americans in Mathematics

Author : Nathaniel Dean
Publisher : American Mathematical Soc.
ISBN 13 : 9780821870792
Total Pages : 224 pages
Book Rating : 4.8/5 (77 download)

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Book Synopsis African Americans in Mathematics by : Nathaniel Dean

Download or read book African Americans in Mathematics written by Nathaniel Dean and published by American Mathematical Soc.. This book was released on 1997-01-01 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Advances in the Casimir Effect

Author : Michael Bordag
Publisher : OUP Oxford
ISBN 13 : 0191579882
Total Pages : 769 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Advances in the Casimir Effect by : Michael Bordag

Download or read book Advances in the Casimir Effect written by Michael Bordag and published by OUP Oxford. This book was released on 2009-05-28 with total page 769 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this book is the Casimir effect, a manifestation of zero-point oscillations of the quantum vacuum resulting in forces acting between closely spaced bodies. For the benefit of the reader, the book assembles field-theoretical foundations of this phenomenon, applications of the general theory to real materials, and a comprehensive description of all recently performed measurements of the Casimir force with a comparison between experiment and theory. There is an urgent need for a book of this type, given the increase of interest in forces originating from the quantum vacuum. Numerous new results have been obtained in the last few years which are not reflected in previous books on the subject, but which are very promising for fundamental science and nanotechnology. The book is a unique source of information presenting a critical assessment of all the main results and approaches from hundreds of journal papers. It also outlines new ideas which have not yet been universally accepted but which are finding increasing support from experiment.

Regularised Integrals, Sums and Traces

Author : Sylvie Paycha
Publisher : American Mathematical Soc.
ISBN 13 : 0821853678
Total Pages : 203 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Regularised Integrals, Sums and Traces by : Sylvie Paycha

Download or read book Regularised Integrals, Sums and Traces written by Sylvie Paycha and published by American Mathematical Soc.. This book was released on 2012 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: ``Regularization techniques'' is the common name for a variety of methods used to make sense of divergent series, divergent integrals, or traces of linear operators in infinite-dimensional spaces. Such methods are often indispensable in problems of number theory, geometry, quantum field theory, and other areas of mathematics and theoretical physics. However arbitrary and noncanonical they might seem at first glance, regularized sums, integrals, and traces often contain canonical concepts, and the main purpose of this book is to illustrate and explain this. This book provides a unified and self-contained mathematical treatment of various regularization techniques. The author shows how to derive regularized sums, integrals, and traces from certain canonical building blocks of the original divergent object. In the process of putting together these ``building blocks'', one encounters many problems and ambiguities caused by various so-called anomalies, which are investigated and explained in detail. Nevertheless, it turns out that the corresponding canonical sums, integrals, sums, and traces are well behaved, thus making the regularization procedure possible and manageable. This new unified outlook on regularization techniques in various fields of mathematics and in quantum field theory can serve as an introduction for anyone from a beginning mathematician interested in the subject to an experienced physicist who wants to gain a unified outlook on techniques he/she uses on a daily basis.

Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II

Author : David Carfi
Publisher : American Mathematical Soc.
ISBN 13 : 0821891480
Total Pages : 384 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II by : David Carfi

Download or read book Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II written by David Carfi and published by American Mathematical Soc.. This book was released on 2013-10-24 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoît Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry and various aspects of dynamical systems in applied mathematics and the applications to other sciences. Also included are articles discussing a variety of connections between these subjects and various areas of physics, engineering, computer science, technology, economics and finance, as well as of mathematics (including probability theory in relation with statistical physics and heat kernel estimates, geometric measure theory, partial differential equations in relation with condensed matter physics, global analysis on non-smooth spaces, the theory of billiards, harmonic analysis and spectral geometry). The companion volume (Contemporary Mathematics, Volume 600) focuses on the more mathematical aspects of fractal geometry and dynamical systems.

Group Theoretical Methods In Physics - Proceedings Of The Yamada Conference Xl And Xx International Colloquium

Author : Tohru Eguchi
Publisher : World Scientific
ISBN 13 : 9814549908
Total Pages : 546 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Group Theoretical Methods In Physics - Proceedings Of The Yamada Conference Xl And Xx International Colloquium by : Tohru Eguchi

Download or read book Group Theoretical Methods In Physics - Proceedings Of The Yamada Conference Xl And Xx International Colloquium written by Tohru Eguchi and published by World Scientific. This book was released on 1995-05-11 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topics discussed in this volume are: Symmetry and Foundations in Classical and Quantum Mechanics; Geometry, Topology and Quantum Field Theory; Quantum Groups and Infinite-Dimensional Lie Algebras; Algebraic Approach to Nuclear Structure; Integrable Statistical Systems and Theory of Critical Phenomena Supersymmetry; Atomic and Molecular Physics; Condensed Matter Physics; Other Applications of Group Theory to Physics.