A Window Into Zeta And Modular Physics
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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.
Some Musings On Theta Eta And Zeta
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Author : Floyd L. Williams
language : en
Publisher: Springer Nature
Release Date :
Some Musings On Theta Eta And Zeta written by Floyd L. Williams and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Zeta Functions Topology And Quantum Physics
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Author : Takashi Aoki
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-10
Zeta Functions Topology And Quantum Physics written by Takashi Aoki 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 2008-05-10 with Mathematics categories.
This volume contains papers by invited speakers of the symposium "Zeta Functions, Topology and Quantum Physics" held at Kinki U- versity in Osaka, Japan, during the period of March 3-6, 2003. The aims of this symposium were to establish mutual understanding and to exchange ideas among researchers working in various fields which have relation to zeta functions and zeta values. We are very happy to add this volume to the series Developments in Mathematics from Springer. In this respect, Professor Krishnaswami Alladi helped us a lot by showing his keen and enthusiastic interest in publishing this volume and by contributing his paper with Alexander Berkovich. We gratefully acknowledge financial support from Kinki University. We would like to thank Professor Megumu Munakata, Vice-Rector of Kinki University, and Professor Nobuki Kawashima, Director of School of Interdisciplinary Studies of Science and Engineering, Kinki Univ- sity, for their interest and support. We also thank John Martindale of Springer for his excellent editorial work.
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).
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.
Lumen Naturae
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Author : Matilde Marcolli
language : en
Publisher: MIT Press
Release Date : 2020-05-26
Lumen Naturae written by Matilde Marcolli and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-26 with Mathematics categories.
Exploring common themes in modern art, mathematics, and science, including the concept of space, the notion of randomness, and the shape of the cosmos. This is a book about art—and a book about mathematics and physics. In Lumen Naturae (the title refers to a purely immanent, non-supernatural form of enlightenment), mathematical physicist Matilde Marcolli explores common themes in modern art and modern science—the concept of space, the notion of randomness, the shape of the cosmos, and other puzzles of the universe—while mapping convergences with the work of such artists as Paul Cezanne, Mark Rothko, Sol LeWitt, and Lee Krasner. Her account, focusing on questions she has investigated in her own scientific work, is illustrated by more than two hundred color images of artworks by modern and contemporary artists. Thus Marcolli finds in still life paintings broad and deep philosophical reflections on space and time, and connects notions of space in mathematics to works by Paul Klee, Salvador Dalí, and others. She considers the relation of entropy and art and how notions of entropy have been expressed by such artists as Hans Arp and Fernand Léger; and traces the evolution of randomness as a mode of artistic expression. She analyzes the relation between graphical illustration and scientific text, and offers her own watercolor-decorated mathematical notebooks. Throughout, she balances discussions of science with explorations of art, using one to inform the other. (She employs some formal notation, which can easily be skipped by general readers.) Marcolli is not simply explaining art to scientists and science to artists; she charts unexpected interdependencies that illuminate the universe.
Harmonic Analysis On Symmetric Spaces Euclidean Space The Sphere And The Poincar Upper Half Plane
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Author : Audrey Terras
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-12
Harmonic Analysis On Symmetric Spaces Euclidean Space The Sphere And The Poincar Upper Half Plane written by Audrey Terras 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 2013-09-12 with Mathematics categories.
This unique text is an introduction to harmonic analysis on the simplest symmetric spaces, namely Euclidean space, the sphere, and the Poincaré upper half plane. This book is intended for beginning graduate students in mathematics or researchers in physics or engineering. Written with an informal style, the book places an emphasis on motivation, concrete examples, history, and, above all, applications in mathematics, statistics, physics, and engineering. Many corrections and updates have been incorporated in this new edition. Updates include discussions of P. Sarnak and others' work on quantum chaos, the work of T. Sunada, Marie-France Vignéras, Carolyn Gordon, and others on Mark Kac's question "Can you hear the shape of a drum?", A. Lubotzky, R. Phillips and P. Sarnak's examples of Ramanujan graphs, and, finally, the author's comparisons of continuous theory with the finite analogues. Topics featured throughout the text include inversion formulas for Fourier transforms, central limit theorems, Poisson's summation formula and applications in crystallography and number theory, applications of spherical harmonic analysis to the hydrogen atom, the Radon transform, non-Euclidean geometry on the Poincaré upper half plane H or unit disc and applications to microwave engineering, fundamental domains in H for discrete groups Γ, tessellations of H from such discrete group actions, automorphic forms, and the Selberg trace formula and its applications in spectral theory as well as number theory.
Algebraic Combinatorics And The Monster Group
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Author : Alexander A. Ivanov
language : en
Publisher: Cambridge University Press
Release Date : 2023-08-17
Algebraic Combinatorics And The Monster Group written by Alexander A. Ivanov 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 2023-08-17 with Mathematics categories.
The current state of knowledge on the Monster group, including Majorana theory, Vertex Operator Algebras, Moonshine and maximal subgroups.
The Sine Gordon Model And Its Applications
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Author : Jesús Cuevas-Maraver
language : en
Publisher: Springer
Release Date : 2014-07-22
The Sine Gordon Model And Its Applications written by Jesús Cuevas-Maraver and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-22 with Science categories.
The sine-Gordon model is a ubiquitous model of Mathematical Physics with a wide range of applications extending from coupled torsion pendula and Josephson junction arrays to gravitational and high-energy physics models. The purpose of this book is to present a summary of recent developments in this field, incorporating both introductory background material, but also with a strong view towards modern applications, recent experiments, developments regarding the existence, stability, dynamics and asymptotics of nonlinear waves that arise in the model. This book is of particular interest to a wide range of researchers in this field, but serves as an introductory text for young researchers and students interested in the topic. The book consists of well-selected thematic chapters on diverse mathematical and physical aspects of the equation carefully chosen and assigned.
Differential And Difference Equations With Applications
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Author : Sandra Pinelas
language : en
Publisher: Springer
Release Date : 2018-05-08
Differential And Difference Equations With Applications written by Sandra Pinelas and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-08 with Mathematics categories.
This book gathers papers from the International Conference on Differential & Difference Equations and Applications 2017 (ICDDEA 2017), held in Lisbon, Portugal on June 5-9, 2017. The editors have compiled the strongest research presented at the conference, providing readers with valuable insights into new trends in the field, as well as applications and high-level survey results. The goal of the ICDDEA was to promote fruitful collaborations between researchers in the fields of differential and difference equations. All areas of differential and difference equations are represented, with a special emphasis on applications.