From Number Theory to Physics

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

Publisher: Springer Science & Business Media

ISBN: 3662028387

Category: Science

Page: 690

View: 4168


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

Author: S. Sternberg

Publisher: Cambridge University Press

ISBN: 9780521558853

Category: Mathematics

Page: 429

View: 3471


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.

Group Theory and Its Application to Physical Problems

Author: Morton Hamermesh

Publisher: Courier Corporation

ISBN: 0486140393

Category: Science

Page: 544

View: 5075


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.

Number Theory in Science and Communication

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

Author: Manfred Schroeder

Publisher: Springer Science & Business Media

ISBN: 3540852972

Category: Science

Page: 431

View: 4049


"Number Theory in Science and Communication" is a well-known introduction for non-mathematicians to this fascinating and useful branch of applied mathematics . It 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, pseudo primes and primitive elements. Their applications to problems in the real world are one of the main themes of the book. This revised fifth edition is augmented by recent advances in coding theory, permutations and derangements and a chapter in quantum cryptography. From reviews of earlier editions – "I continue to find [Schroeder’s] Number Theory a goldmine of valuable information. It is a marvelous book, in touch with the most recent applications of number theory and written with great clarity and humor.’ Philip Morrison (Scientific American) "A light-hearted and readable volume with a wide range of applications to which the author has been a productive contributor – useful mathematics outside the formalities of theorem and proof." Martin Gardner

Group Theory and Quantum Mechanics

Author: Michael Tinkham

Publisher: Courier Corporation

ISBN: 0486131661

Category: Science

Page: 352

View: 8062


Graduate-level text develops group theory relevant to physics and chemistry and illustrates their applications to quantum mechanics, with systematic treatment of quantum theory of atoms, molecules, solids. 1964 edition.

Number Theory and Physics

Proceedings of the Winter School, Les Houches, France, March 7–16, 1989

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

Publisher: Springer Science & Business Media

ISBN: 3642754058

Category: Science

Page: 311

View: 7117


7 Les Houches Number theory, or arithmetic, sometimes referred to as the queen of mathematics, is often considered as the purest branch of mathematics. It also has the false repu tation of being without any application to other areas of knowledge. Nevertheless, throughout their history, physical and natural sciences have experienced numerous unexpected relationships to number theory. The book entitled Number Theory in Science and Communication, by M.R. Schroeder (Springer Series in Information Sciences, Vol. 7, 1984) provides plenty of examples of cross-fertilization between number theory and a large variety of scientific topics. The most recent developments of theoretical physics have involved more and more questions related to number theory, and in an increasingly direct way. This new trend is especially visible in two broad families of physical problems. The first class, dynamical systems and quasiperiodicity, includes classical and quantum chaos, the stability of orbits in dynamical systems, K.A.M. theory, and problems with "small denominators", as well as the study of incommensurate structures, aperiodic tilings, and quasicrystals. The second class, which includes the string theory of fundamental interactions, completely integrable models, and conformally invariant two-dimensional field theories, seems to involve modular forms and p adic numbers in a remarkable way.

Groups, Representations and Physics

Author: H.F Jones

Publisher: CRC Press

ISBN: 9781420050295

Category: Mathematics

Page: 340

View: 3832


Illustrating the fascinating interplay between physics and mathematics, Groups, Representations and Physics, Second Edition provides a solid foundation in the theory of groups, particularly group representations. For this new, fully revised edition, the author has enhanced the book's usefulness and widened its appeal by adding a chapter on the Cartan-Dynkin treatment of Lie algebras. This treatment, a generalization of the method of raising and lowering operators used for the rotation group, leads to a systematic classification of Lie algebras and enables one to enumerate and construct their irreducible representations. Taking an approach that allows physics students to recognize the power and elegance of the abstract, axiomatic method, the book focuses on chapters that develop the formalism, followed by chapters that deal with the physical applications. It also illustrates formal mathematical definitions and proofs with numerous concrete examples.

Group Theory in Physics

Author: J. F. Cornwell

Publisher: Academic Pr


Category: Group theory

Page: 628

View: 8464


Recent devopments, particularly in high-energy physics, have projected group theory and symmetry consideration into a central position in theoretical physics. These developments have taken physicists increasingly deeper into the fascinating world of pure mathematics. This work presents important mathematical developments of the last fifteen years in a form that is easy to comprehend and appreciate.

Group Theory in Physics

An Introduction to Symmetry Principles, Group Representations, and Special Functions in Classical and Quantum Physics

Author: Wu-Ki Tung

Publisher: World Scientific Publishing Company

ISBN: 981310404X

Category: Representations of groups

Page: 336

View: 3439


An introductory text book for graduates and advanced undergraduates on group representation theory. It emphasizes group theory's role as the mathematical framework for describing symmetry properties of classical and quantum mechanical systems. Familiarity with basic group concepts and techniques is invaluable in the education of a modern-day physicist. This book emphasizes general features and methods which demonstrate the power of the group-theoretical approach in exposing the systematics of physical systems with associated symmetry. Particular attention is given to pedagogy. In developing the theory, clarity in presenting the main ideas and consequences is given the same priority as comprehensiveness and strict rigor. To preserve the integrity of the mathematics, enough technical information is included in the appendices to make the book almost self-contained. A set of problems and solutions has been published in a separate booklet. Request Inspection Copy

An Adventurer's Guide to Number Theory

Author: Richard Friedberg

Publisher: Courier Corporation

ISBN: 0486152693

Category: Science

Page: 240

View: 8989


This witty introduction to number theory deals with the properties of numbers and numbers as abstract concepts. Topics include primes, divisibility, quadratic forms, and related theorems.


An Introduction to Group Theory and Its Applications

Author: R. McWeeny

Publisher: Elsevier

ISBN: 1483226247

Category: Mathematics

Page: 262

View: 6795


Symmetry: An Introduction to Group Theory and its Application is an eight-chapter text that covers the fundamental bases, the development of the theoretical and experimental aspects of the group theory. Chapter 1 deals with the elementary concepts and definitions, while Chapter 2 provides the necessary theory of vector spaces. Chapters 3 and 4 are devoted to an opportunity of actually working with groups and representations until the ideas already introduced are fully assimilated. Chapter 5 looks into the more formal theory of irreducible representations, while Chapter 6 is concerned largely with quadratic forms, illustrated by applications to crystal properties and to molecular vibrations. Chapter 7 surveys the symmetry properties of functions, with special emphasis on the eigenvalue equation in quantum mechanics. Chapter 8 covers more advanced applications, including the detailed analysis of tensor properties and tensor operators. This book is of great value to mathematicians, and math teachers and students.

Number theory and physics

proceedings of the winter school, Les Houches, France, March 7-16, 1989

Author: Jean Marc Luck,Pierre Moussa,Michel Waldschmidt

Publisher: Springer Verlag


Category: Mathematics

Page: 311

View: 5190


Group Theory and Its Applications in Physics

Author: Teturo Inui,Yukito Tanabe,Yositaka Onodera

Publisher: Springer Science & Business Media

ISBN: 3642800211

Category: Science

Page: 397

View: 9785


This book has been written to introduce readers to group theory and its ap plications in atomic physics, molecular physics, and solid-state physics. The first Japanese edition was published in 1976. The present English edi tion has been translated by the authors from the revised and enlarged edition of 1980. In translation, slight modifications have been made in. Chaps. 8 and 14 to update and condense the contents, together with some minor additions and improvements throughout the volume. The authors cordially thank Professor J. L. Birman and Professor M. Car dona, who encouraged them to prepare the English translation. Tokyo, January 1990 T. Inui . Y. Tanabe Y. Onodera Preface to the Japanese Edition As the title shows, this book has been prepared as a textbook to introduce readers to the applications of group theory in several fields of physics. Group theory is, in a nutshell, the mathematics of symmetry. It has three main areas of application in modern physics. The first originates from early studies of crystal morphology and constitutes a framework for classical crystal physics. The analysis of the symmetry of tensors representing macroscopic physical properties (such as elastic constants) belongs to this category. The sec ond area was enunciated by E. Wigner (1926) as a powerful means of handling quantum-mechanical problems and was first applied in this sense to the analysis of atomic spectra. Soon, H.

Theoretical Physics

Author: Georg Joos,Ira M. Freeman

Publisher: Courier Corporation

ISBN: 0486318532

Category: Science

Page: 928

View: 7330


Classic treatise covers mathematical topics needed by theoretical and experimental physicists (vector analysis, calculus of variations, etc.), followed by coverage of mechanics, electromagnetic theory, thermodynamics, quantum mechanics, and nuclear physics.

An Introduction to Tensors and Group Theory for Physicists

Author: Nadir Jeevanjee

Publisher: Birkhäuser

ISBN: 3319147943

Category: Science

Page: 305

View: 4705


The second edition of this highly praised textbook provides an introduction to tensors, group theory, and their applications in classical and quantum physics. Both intuitive and rigorous, it aims to demystify tensors by giving the slightly more abstract but conceptually much clearer definition found in the math literature, and then connects this formulation to the component formalism of physics calculations. New pedagogical features, such as new illustrations, tables, and boxed sections, as well as additional “invitation” sections that provide accessible introductions to new material, offer increased visual engagement, clarity, and motivation for students. Part I begins with linear algebraic foundations, follows with the modern component-free definition of tensors, and concludes with applications to physics through the use of tensor products. Part II introduces group theory, including abstract groups and Lie groups and their associated Lie algebras, then intertwines this material with that of Part I by introducing representation theory. Examples and exercises are provided in each chapter for good practice in applying the presented material and techniques. Prerequisites for this text include the standard lower-division mathematics and physics courses, though extensive references are provided for the motivated student who has not yet had these. Advanced undergraduate and beginning graduate students in physics and applied mathematics will find this textbook to be a clear, concise, and engaging introduction to tensors and groups. Reviews of the First Edition “[P]hysicist Nadir Jeevanjee has produced a masterly book that will help other physicists understand those subjects [tensors and groups] as mathematicians understand them... From the first pages, Jeevanjee shows amazing skill in finding fresh, compelling words to bring forward the insight that animates the modern mathematical view...[W]ith compelling force and clarity, he provides many carefully worked-out examples and well-chosen specific problems... Jeevanjee’s clear and forceful writing presents familiar cases with a freshness that will draw in and reassure even a fearful student. [This] is a masterpiece of exposition and explanation that would win credit for even a seasoned author.” —Physics Today "Jeevanjee’s [text] is a valuable piece of work on several counts, including its express pedagogical service rendered to fledgling physicists and the fact that it does indeed give pure mathematicians a way to come to terms with what physicists are saying with the same words we use, but with an ostensibly different meaning. The book is very easy to read, very user-friendly, full of examples...and exercises, and will do the job the author wants it to do with style.” —MAA Reviews

Group Theory in a Nutshell for Physicists

Author: A. Zee

Publisher: Princeton University Press

ISBN: 1400881188

Category: Science

Page: 632

View: 7732


Although group theory is a mathematical subject, it is indispensable to many areas of modern theoretical physics, from atomic physics to condensed matter physics, particle physics to string theory. In particular, it is essential for an understanding of the fundamental forces. Yet until now, what has been missing is a modern, accessible, and self-contained textbook on the subject written especially for physicists. Group Theory in a Nutshell for Physicists fills this gap, providing a user-friendly and classroom-tested text that focuses on those aspects of group theory physicists most need to know. From the basic intuitive notion of a group, A. Zee takes readers all the way up to how theories based on gauge groups could unify three of the four fundamental forces. He also includes a concise review of the linear algebra needed for group theory, making the book ideal for self-study. Provides physicists with a modern and accessible introduction to group theory Covers applications to various areas of physics, including field theory, particle physics, relativity, and much more Topics include finite group and character tables; real, pseudoreal, and complex representations; Weyl, Dirac, and Majorana equations; the expanding universe and group theory; grand unification; and much more The essential textbook for students and an invaluable resource for researchers Features a brief, self-contained treatment of linear algebra An online illustration package is available to professors Solutions manual (available only to professors)

The Trouble With Physics

The Rise of String Theory, the Fall of a Science, and What Comes Next

Author: Lee Smolin

Publisher: HMH

ISBN: 9780547348483

Category: Science

Page: 416

View: 1449


“A splendid, edifying report from the front lines of theorectical physics” (San Francisco Chronicle). In this illuminating book, renowned physicist Lee Smolin argues that fundamental physics—the search for the laws of nature—is losing its way. Ambitious ideas about extra dimensions, exotic particles, multiple universes, and strings have captured the public’s imagination—and the imagination of experts. But these ideas have not been tested experimentally, and some, like string theory, seem to offer no possibility of being tested. Even still, these speculations dominate the field, attracting the best talent and much of the funding, while creating a climate in which emerging physicists are often penalized for pursuing other avenues. The situation threatens to impede the very progress of science. With clarity, passion, and authority, Smolin offers an unblinking assessment of the troubles that face modern physics, and an encouraging view of where the search for the next big idea may lead. “The best book about contemporary science written for the layman that I have ever read.” —The Times (London)

The Little Book of String Theory

Author: Steven S. Gubser

Publisher: Princeton University Press

ISBN: 9781400834433

Category: Science

Page: 184

View: 1989


The Little Book of String Theory offers a short, accessible, and entertaining introduction to one of the most talked-about areas of physics today. String theory has been called the "theory of everything." It seeks to describe all the fundamental forces of nature. It encompasses gravity and quantum mechanics in one unifying theory. But it is unproven and fraught with controversy. After reading this book, you'll be able to draw your own conclusions about string theory. Steve Gubser begins by explaining Einstein's famous equation E = mc2 , quantum mechanics, and black holes. He then gives readers a crash course in string theory and the core ideas behind it. In plain English and with a minimum of mathematics, Gubser covers strings, branes, string dualities, extra dimensions, curved spacetime, quantum fluctuations, symmetry, and supersymmetry. He describes efforts to link string theory to experimental physics and uses analogies that nonscientists can understand. How does Chopin's Fantasie-Impromptu relate to quantum mechanics? What would it be like to fall into a black hole? Why is dancing a waltz similar to contemplating a string duality? Find out in the pages of this book. The Little Book of String Theory is the essential, most up-to-date beginner's guide to this elegant, multidimensional field of physics.

Applied Group Theory

For Physicists and Chemists

Author: George H. Duffey

Publisher: Courier Corporation

ISBN: 0486783146

Category: Science

Page: 384

View: 4554


This text introduces advanced undergraduates and graduate students to key applications of group theory. Topics include the nature of symmetry operations; applications to vibrating systems, continuum mechanics, and quantum structures; permutation, continuous, and rotation groups; and physical Lie algebras. Each chapter concludes with a concise review, discussion questions, problems, and references. 1992 edition.