From Number Theory to Physics

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Author: Pierre Cartier,Centre de Physique

Publisher: Springer

ISBN: 9780387533421

Category: Mathematics

Page: 690

View: 9253

From Number Theory to Physics

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Author: Michel Waldschmidt,Pierre Moussa,Jean-Marc Luck,Claude Itzykson

Publisher: Springer Science & Business Media

ISBN: 3662028387

Category: Science

Page: 690

View: 9797

The present book contains fourteen expository contributions on various topics connected to Number Theory, or Arithmetics, and its relationships to Theoreti cal Physics. The first part is mathematically oriented; it deals mostly with ellip tic curves, modular forms, zeta functions, Galois theory, Riemann surfaces, and p-adic analysis. The second part reports on matters with more direct physical interest, such as periodic and quasiperiodic lattices, or classical and quantum dynamical systems. The contribution of each author represents a short self-contained course on a specific subject. With very few prerequisites, the reader is offered a didactic exposition, which follows the author's original viewpoints, and often incorpo rates the most recent developments. As we shall explain below, there are strong relationships between the different chapters, even though every single contri bution can be read independently of the others. This volume originates in a meeting entitled Number Theory and Physics, which took place at the Centre de Physique, Les Houches (Haute-Savoie, France), on March 7 - 16, 1989. The aim of this interdisciplinary meeting was to gather physicists and mathematicians, and to give to members of both com munities the opportunity of exchanging ideas, and to benefit from each other's specific knowledge, in the area of Number Theory, and of its applications to the physical sciences. Physicists have been given, mostly through the program of lectures, an exposition of some of the basic methods and results of Num ber Theory which are the most actively used in their branch.

Group Theory and Physics

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Author: S. Sternberg

Publisher: Cambridge University Press

ISBN: 9780521558853

Category: Mathematics

Page: 429

View: 1331

This book is an introduction to group theory and its application to physics. The author considers the physical applications and develops mathematical theory in a presentation that is unusually cohesive and well-motivated. The book discusses many modern topics including molecular vibrations, homogeneous vector bundles, compact groups and Lie groups, and there is much discussion of the group SU(n) and its representations, which is of great significance in elementary particle physics. The author also considers applications to solid-state physics. This is an essential resource for senior undergraduates and researchers in physics and applied mathematics.

Frontiers in Number Theory, Physics, and Geometry II

On Conformal Field Theories, Discrete Groups and Renormalization

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Author: Pierre E. Cartier,Bernard Julia,Pierre Moussa,Pierre Vanhove

Publisher: Springer Science & Business Media

ISBN: 3540303081

Category: Mathematics

Page: 789

View: 737

Ten years after a 1989 meeting of number theorists and physicists at the Centre de Physique des Houches, a second event focused on the broader interface of number theory, geometry, and physics. This book is the first of two volumes resulting from that meeting. Broken into three parts, it covers Conformal Field Theories, Discrete Groups, and Renormalization, offering extended versions of the lecture courses and shorter texts on special topics.

Frontiers in Number Theory, Physics, and Geometry I

On Random Matrices, Zeta Functions, and Dynamical Systems

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Author: Pierre E. Cartier,Bernard Julia,Pierre Moussa,Pierre Vanhove

Publisher: Springer

ISBN: 9783540231899

Category: Mathematics

Page: 624

View: 926

The relation between mathematics and physics has a long history, in which the role of number theory and of other more abstract parts of mathematics has recently become more prominent. More than 10 years after a first meeting between number theorists and physicists at the Centre de Physique des Houches, a second two-week event focused on the broader interface of number theory, geometry, and physics. This book collects the material presented at this meeting.

Group Theory and Its Application to Physical Problems

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Author: Morton Hamermesh

Publisher: Courier Corporation

ISBN: 0486140393

Category: Science

Page: 544

View: 8401

One of the best-written, most skillful expositions of group theory and its physical applications, directed primarily to advanced undergraduate and graduate students in physics, especially quantum physics. With problems.

Surveys in Number Theory

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Author: Krishnaswami Alladi

Publisher: Springer Science & Business Media

ISBN: 0387785108

Category: Mathematics

Page: 188

View: 6470

Number theory has a wealth of long-standing problems, the study of which over the years has led to major developments in many areas of mathematics. This volume consists of seven significant chapters on number theory and related topics. Written by distinguished mathematicians, key topics focus on multipartitions, congruences and identities (G. Andrews), the formulas of Koshliakov and Guinand in Ramanujan's Lost Notebook (B. C. Berndt, Y. Lee, and J. Sohn), alternating sign matrices and the Weyl character formulas (D. M. Bressoud), theta functions in complex analysis (H. M. Farkas), representation functions in additive number theory (M. B. Nathanson), and mock theta functions, ranks, and Maass forms (K. Ono), and elliptic functions (M. Waldschmidt).

Dynamical Systems, Number Theory and Applications

A Festschrift in Honor of Armin Leutbecher's 80th Birthday

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Author: Thomas Hagen,Florian Rupp,Jrgen Scheurle

Publisher: World Scientific

ISBN: 981469987X

Category: Mathematics

Page: 266

View: 1075

"This volume consists of a selection of research-type articles on dynamical systems, evolution equations, analytic number theory and closely related topics. A strong emphasis is on a fair balance between theoretical and more applied work, thus spanning the chasm between abstract insight and actual application. Several of the articles are expected to be in the intersection of dynamical systems theory and number theory. One article will likely relate the topics presented to the academic achievements and interests of Prof. Leutbecher and shed light on common threads among all the contributions."--

Number Theory in Science and Communication

With Applications in Cryptography, Physics, Digital Information, Computing and Self-similarity

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Author: Manfred Robert Schroeder

Publisher: Springer Science & Business Media

ISBN: 9783540620068

Category: Mathematics

Page: 362

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Number Theory in Science and Communication is an introduction for non-mathematicians. The book stresses intuitive understanding rather than abstract theory and highlights important concepts such as continued fractions, the golden ratio, quadratic residues and Chinese remainders, trapdoor functions, pseudoprimes and primituve elements. Their applications to problems in the real world is one of the main themes of the book. This third edition is augmented by recent advances in primes in progressions, twin primes, prime triplets, prime quadruplets and quintruplets, factoring with elliptic curves, quantum factoring, Golomb rulers and "baroque" integers.

Lie Theory and Its Applications in Physics

IX International Workshop

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Author: Vladimir Dobrev

Publisher: Springer Science & Business Media

ISBN: 4431542701

Category: Mathematics

Page: 554

View: 1725

Traditionally, Lie Theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrisation of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry which is very helpful in understanding its structure. Geometrisation and symmetries are meant in their broadest sense, i.e., classical geometry, differential geometry, groups and quantum groups, infinite-dimensional (super-)algebras, and their representations. Furthermore, we include the necessary tools from functional analysis and number theory. This is a large interdisciplinary and interrelated field. Samples of these new trends are presented in this volume, based on contributions from the Workshop “Lie Theory and Its Applications in Physics” held near Varna, Bulgaria, in June 2011. This book is suitable for an extensive audience of mathematicians, mathematical physicists, theoretical physicists, and researchers in the field of Lie Theory.