Zeta Functions Topology And Quantum Physics

Author : Takashi Aoki,Shigeru Kanemitsu,Mikio Nakahara,Yasuo Ohno
Publisher : Springer Science & Business Media
Page : 219 pages
File Size : 46,8 Mb
Release : 2008-05-10
Category : Mathematics
ISBN : 9780387249810

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Zeta Functions, Topology and Quantum Physics by Takashi Aoki,Shigeru Kanemitsu,Mikio Nakahara,Yasuo Ohno Pdf

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.

Author : Takashi Aoki,Shigeru Kanemitsu,Mikio Nakahara,Yasuo Ohno
Publisher : Springer
Page : 0 pages
File Size : 53,8 Mb
Release : 2008-11-01
Category : Mathematics
ISBN : 0387522883

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Zeta Functions, Topology and Quantum Physics by Takashi Aoki,Shigeru Kanemitsu,Mikio Nakahara,Yasuo Ohno Pdf

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.

Author : Carsten Schneider,Johannes Blümlein
Publisher : Springer Science & Business Media
Page : 411 pages
File Size : 53,8 Mb
Release : 2013-10-05
Category : Science
ISBN : 9783709116166

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Computer Algebra in Quantum Field Theory by Carsten Schneider,Johannes Blümlein Pdf

The book focuses on advanced computer algebra methods and special functions that have striking applications in the context of quantum field theory. It presents the state of the art and new methods for (infinite) multiple sums, multiple integrals, in particular Feynman integrals, difference and differential equations in the format of survey articles. The presented techniques emerge from interdisciplinary fields: mathematics, computer science and theoretical physics; the articles are written by mathematicians and physicists with the goal that both groups can learn from the other field, including most recent developments. Besides that, the collection of articles also serves as an up-to-date handbook of available algorithms/software that are commonly used or might be useful in the fields of mathematics, physics or other sciences.

Author : Shigeru Kanemitsu,Haruo Tsukada
Publisher : World Scientific
Page : 316 pages
File Size : 49,8 Mb
Release : 2015
Category : Mathematics
ISBN : 9789814449625

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Contributions to the Theory of Zeta-Functions by Shigeru Kanemitsu,Haruo Tsukada Pdf

This volume provides a systematic survey of almost all the equivalent assertions to the functional equations - zeta symmetry - which zeta-functions satisfy, thus streamlining previously published results on zeta-functions. The equivalent relations are given in the form of modular relations in Fox H-function series, which at present include all that have been considered as candidates for ingredients of a series. The results are presented in a clear and simple manner for readers to readily apply without much knowledge of zeta-functions. This volume aims to keep a record of the 150-year-old heritage starting from Riemann on zeta-functions, which are ubiquitous in all mathematical sciences, wherever there is a notion of the norm. It provides almost all possible equivalent relations to the zeta-functions without requiring a reader's deep knowledge on their definitions. This can be an ideal reference book for those studying zeta-functions.

Author : Dmitri Fursaev,Dmitri Vassilevich
Publisher : Springer Science & Business Media
Page : 294 pages
File Size : 53,9 Mb
Release : 2011-06-25
Category : Science
ISBN : 9789400702059

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Operators, Geometry and Quanta by Dmitri Fursaev,Dmitri Vassilevich Pdf

This book gives a detailed and self-contained introduction into the theory of spectral functions, with an emphasis on their applications to quantum field theory. All methods are illustrated with applications to specific physical problems from the forefront of current research, such as finite-temperature field theory, D-branes, quantum solitons and noncommutativity. In the first part of the book, necessary background information on differential geometry and quantization, including less standard material, is collected. The second part of the book contains a detailed description of main spectral functions and methods of their calculation. In the third part, the theory is applied to several examples (D-branes, quantum solitons, anomalies, noncommutativity). This book addresses advanced graduate students and researchers in mathematical physics with basic knowledge of quantum field theory and differential geometry. The aim is to prepare readers to use spectral functions in their own research, in particular in relation to heat kernels and zeta functions.

Author : Floyd Williams
Publisher : Springer Science & Business Media
Page : 394 pages
File Size : 42,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461200093

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Topics in Quantum Mechanics by Floyd Williams Pdf

This self-contained text presents quantum mechanics from the point of view of some computational examples with a mixture of mathematical clarity often not found in texts offering only a purely physical point of view. Emphasis is placed on the systematic application of the Nikiforov-- Uvarov theory of generalized hypergeometric differential equations to solve the Schr"dinger equation and to obtain the quantization of energies from a single unified point of view.

Author : Jianqiang Zhao
Publisher : World Scientific
Page : 620 pages
File Size : 48,6 Mb
Release : 2016-03-07
Category : Mathematics
ISBN : 9789814689410

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Multiple Zeta Functions, Multiple Polylogarithms and Their Special Values by Jianqiang Zhao Pdf

This is the first introductory book on multiple zeta functions and multiple polylogarithms which are the generalizations of the Riemann zeta function and the classical polylogarithms, respectively, to the multiple variable setting. It contains all the basic concepts and the important properties of these functions and their special values. This book is aimed at graduate students, mathematicians and physicists who are interested in this current active area of research. The book will provide a detailed and comprehensive introduction to these objects, their fascinating properties and interesting relations to other mathematical subjects, and various generalizations such as their q-analogs and their finite versions (by taking partial sums modulo suitable prime powers). Historical notes and exercises are provided at the end of each chapter. Contents:Multiple Zeta FunctionsMultiple Polylogarithms (MPLs)Multiple Zeta Values (MZVs)Drinfeld Associator and Single-Valued MZVsMultiple Zeta Value IdentitiesSymmetrized Multiple Zeta Values (SMZVs)Multiple Harmonic Sums (MHSs) and Alternating VersionFinite Multiple Zeta Values and Finite Euler Sumsq-Analogs of Multiple Harmonic (Star) Sums Readership: Advanced undergraduates and graduate students in mathematics, mathematicians interested in multiple zeta values. Key Features:For the first time, a detailed explanation of the theory of multiple zeta values is given in book form along with numerous illustrations in explicit examplesThe book provides for the first time a comprehensive introduction to multiple polylogarithms and their special values at roots of unity, from the basic definitions to the more advanced topics in current active researchThe book contains a few quite intriguing results relating the special values of multiple zeta functions and multiple polylogarithms to other branches of mathematics and physics, such as knot theory and the theory of motivesMany exercises contain supplementary materials which deepens the reader's understanding of the main text

Author : Louis H Kauffman,Randy A Baadhio
Publisher : World Scientific
Page : 392 pages
File Size : 54,5 Mb
Release : 1993-09-15
Category : Science
ISBN : 9789814502672

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Quantum Topology by Louis H Kauffman,Randy A Baadhio Pdf

This book constitutes a review volume on the relatively new subject of Quantum Topology. Quantum Topology has its inception in the 1984/1985 discoveries of new invariants of knots and links (Jones, Homfly and Kauffman polynomials). These invariants were rapidly connected with quantum groups and methods in statistical mechanics. This was followed by Edward Witten's introduction of methods of quantum field theory into the subject and the formulation by Witten and Michael Atiyah of the concept of topological quantum field theories. This book is a review volume of on-going research activity. The papers derive from talks given at the Special Session on Knot and Topological Quantum Field Theory of the American Mathematical Society held at Dayton, Ohio in the fall of 1992. The book consists of a self-contained article by Kauffman, entitled Introduction to Quantum Topology and eighteen research articles by participants in the special session. This book should provide a useful source of ideas and results for anyone interested in the interface between topology and quantum field theory. Contents:Introduction to Quantum Topology (L H Kauffman)Knot Theory, Exotic Spheres and Global Gravitational Anomalies (R A Baadhio)A Diagrammatic Theory of Knotted Surfaces (J S Carter & M Saito)A Categorical Construction of 4D Topological Quantum Field Theories (L Crane & D Yetter)Evaluating the Crane-Yetter Invariant (L Crane, L H Kauffman & D Yetter)A Method for Computing the Arf Invariants of Links (P Gilmer)Triangulations, Categories and Extended Topological Field Theories (R J Lawrence)The Casson Invariant for Two-Fold Branched Covers of Links (D Mullins)Elementary Conjectures in Classical Knot Theory (J H Przytycki)Knot Polynomials as States of Nonperturbative Four Dimensional Quantum Gravity (J Pullin)On Invariants of 3-Manifolds Derived from Abelian Groups (J Mattes, M M Polyak & N Reshetikhin)and other papers Readership: Mathematicians and mathematical physicists. keywords:Quantum Topology;Topological Quantum Field Theory;Meeting;AMS Special Session;Dayton, OH (USA)

Author : A P Balachandran,G Marmo,B S Skagerstam,A Stern
Publisher : World Scientific
Page : 376 pages
File Size : 41,9 Mb
Release : 1991-05-16
Category : Science
ISBN : 9789814506717

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Classical Topology and Quantum States by A P Balachandran,G Marmo,B S Skagerstam,A Stern Pdf

This book is an introduction to the role of topology in the quantization of classical systems. It is also an introduction to topological solitons with special emphasis on Skyrmions. As regards the first aspect, several issues of current interest are dealt with at a reasonably elementary level. Examples are principal fibre bundles and their role in quantum physics, the possibility of spinorial quantum states in a Lagrangian theory based on tensorial variables, and multiply connected configuration spaces and associated quantum phenomena like the QCD q angle and exotic statistics. The ideas are also illustrated by simple examples such as the spinning particle, the charge-monopole system and strings in 3+1 dimensions. The application of these ideas to quantum gravity is another subject treated at an introductory level. An attempt has been made in this book to introduce the reader to the significance of topology for many distinct physical systems such as spinning particles, the charge- monopole system, strings, Skyrmions, QCD and gravity. The book is an outgrowth of lectures given by the authors at various institutions and conferences. Contents:Part I: Classical Mechanics and Quantum States:The Dirac-Bergmann Theory of ConstraintsNonrelativistic Particles with Fixed SpinMagnetic MonopolesThe Canonical Formalism and QuantizationThe Wess-Zumino Term and the Path SpaceQuantum Symmetries and the Wess-Zumino TermQuantum Theory for Multiply Connected Configuration SpacesPart II: Topological Solitons and Nonlinear Models:Topological Solitons in One and Two DimensionsNonlinear Models as Gauge TheoriesThe Chern-Simons TermPart III: Skyrmions:The Effective Lagrangian for QCDSkyrme Solitons for Two FlavoursPreliminary Discussion of Skyrme's ProposalsBaryon Number and Spin of the SkyrmionMore on the Wess-Zumino TermA Hierarchy of “Spherically Symmetric” AnsätzeSkyrmion PhenomenologyElectroweak SkyrmionsPart IV: Gauge, Gravity and String Theories:Multiply Connected Configuration Spaces in Gauge and Gravity TheoriesGeons and their PropertiesStatistics, Strings and Gravity Readership: Mathematical physicists and physicists interested in topological concepts, soliton and skyrmion theory and foundations of quantum theory. keywords:Skyrmions and Other Solitons;Geons;Magnetic Monopoles;Nonlinear Models;Wess-Zumino Term;Topology and Quantum Theory;Chern-Simons Theory;Fibre Bundles;Constraint Theory and Quantization;Spin and Statistics

Author : Takashi Aoki,Shigeru Kanemitsu,Jianya Liu
Publisher : World Scientific
Page : 267 pages
File Size : 40,9 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814289924

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Number Theory by Takashi Aoki,Shigeru Kanemitsu,Jianya Liu Pdf

This volume aims at collecting survey papers which give broad and enlightening perspectives of various aspects of number theory. Kitaoka''s paper is a continuation of his earlier paper published in the last proceedings and pushes the research forward. Browning''s paper introduces a new direction of research on analytic number theory OCo quantitative theory of some surfaces and Bruedern et al ''s paper details state-of-the-art affairs of additive number theory. There are two papers on modular forms OCo Kohnen''s paper describes generalized modular forms (GMF) which has some applications in conformal field theory, while Liu''s paper is very useful for readers who want to have a quick introduction to Maass forms and some analytic-number-theoretic problems related to them. Matsumoto et al ''s paper gives a very thorough survey on functional relations of root system zeta-functions, HoshiOCoMiyake''s paper is a continuation of Miyake''s long and fruitful research on generic polynomials and gives rise to related Diophantine problems, and Jia''s paper surveys some dynamical aspects of a special arithmetic function connected with the distribution of prime numbers. There are two papers of collections of problems by Shparlinski on exponential and character sums and Schinzel on polynomials which will serve as an aid for finding suitable research problems. Yamamura''s paper is a complete bibliography on determinant expressions for a certain class number and will be useful to researchers. Thus the book gives a good-balance of classical and modern aspects in number theory and will be useful to researchers including enthusiastic graduate students. Sample Chapter(s). Chapter 1: Resent Progress on the Quantitative Arithmetic of Del Pezzo Surfaces (329 KB). Contents: Recent Progress on the Quantitative Arithmetic of Del Pezzo Surfaces (T D Browning); Additive Representation in Thin Sequences, VIII: Diophantine Inequalities in Review (J Brdern et al.); Recent Progress on Dynamics of a Special Arithmetic Function (C-H Jia); Some Diophantine Problems Arising from the Isomorphism Problem of Generic Polynomials (A Hoshi & K Miyake); A Statistical Relation of Roots of a Polynomial in Different Local Fields II (Y Kitaoka); Generalized Modular Functions and Their Fourier Coefficients (W Kohnen); Functional Relations for Zeta-Functions of Root Systems (Y Komori et al.); A Quick Introduction to Maass Forms (J-Y Liu); The Number of Non-Zero Coefficients of a Polynomial-Solved and Unsolved Problems (A Schinzel); Open Problems on Exponential and Character Sums (I E Shparlinski); Errata to OC A General Modular Relation in Analytic Number TheoryOCO (H Tsukada); Bibliography on Determinantal Expressions of Relative Class Numbers of Imaginary Abelian Number Fields (K Yamamura). Readership: Graduate students and researchers in mathematics.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 40,6 Mb
Release : 2024-05-17
Category : Electronic
ISBN : 9789814466240

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Number Theory by Anonim Pdf

Author : Yasushi Komori,Kohji Matsumoto,Hirofumi Tsumura
Publisher : Springer Nature
Page : 419 pages
File Size : 41,7 Mb
Release : 2024-02-03
Category : Mathematics
ISBN : 9789819909100

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The Theory of Zeta-Functions of Root Systems by Yasushi Komori,Kohji Matsumoto,Hirofumi Tsumura Pdf

The contents of this book was created by the authors as a simultaneous generalization of Witten zeta-functions, Mordell–Tornheim multiple zeta-functions, and Euler–Zagier multiple zeta-functions. Zeta-functions of root systems are defined by certain multiple series, given in terms of root systems. Therefore, they intrinsically have the action of associated Weyl groups. The exposition begins with a brief introduction to the theory of Lie algebras and root systems and then provides the definition of zeta-functions of root systems, explicit examples associated with various simple Lie algebras, meromorphic continuation and recursive analytic structure described by Dynkin diagrams, special values at integer points, functional relations, and the background given by the action of Weyl groups. In particular, an explicit form of Witten’s volume formula is provided. It is shown that various relations among special values of Euler–Zagier multiple zeta-functions—which usually are called multiple zeta values (MZVs) and are quite important in connection with Zagier’s conjecture—are just special cases of various functional relations among zeta-functions of root systems. The authors further provide other applications to the theory of MZVs and also introduce generalizations with Dirichlet characters, and with certain congruence conditions. The book concludes with a brief description of other relevant topics.

Author : Andrei A. Bytsenko
Publisher : World Scientific
Page : 370 pages
File Size : 54,7 Mb
Release : 2003
Category : Science
ISBN : 9789812383648

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Analytic Aspects of Quantum Fields by Andrei A. Bytsenko Pdf

One of the aims of this book is to explain in a basic manner the seemingly difficult issues of mathematical structure using some specific examples as a guide. In each of the cases considered, a comprehensible physical problem is approached, to which the corresponding mathematical scheme is applied, its usefulness being duly demonstrated. The authors try to fill the gap that always exists between the physics of quantum field theories and the mathematical methods best suited for its formulation, which are increasingly demanding on the mathematical ability of the physicist.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 53,7 Mb
Release : 2024-05-17
Category : Electronic
ISBN : 9789814479257

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Quantum Fluctuations of Spacetime by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 55,6 Mb
Release : 2024-05-17
Category : Electronic
ISBN : 9789814474870

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Number Theory by Anonim Pdf