Topics in Contemporary Mathematical Physics

Author: Kai S. Lam

Publisher: World Scientific

ISBN: 9789812384546

Category: Science

Page: 620

View: 7164

This textbook, pitched at the advanced-undergraduate to beginning-graduate level, focuses on mathematical topics of relevance in contemporary physics that are not usually covered in texts at the same level. Its main purpose is to help students appreciate and take advantage of the modern trend of very productive symbiosis between physics and mathematics. Three major areas are covered: (1) linear operators; (2) group representations and Lie algebra representations; (3) topology and differential geometry.The following are noteworthy features of this book: the style of exposition is a fusion of those common in the standard physics and mathematics literatures; the level of exposition varies from quite elementary to moderately advanced, so that the book is of interest to a wide audience; despite the diversity of the topics covered, there is a strong degree of thematic unity; much care is devoted to detailed cross-referencing so that, from any part of the book, the reader can trace easily where specific concepts or techniques are introduced.

Fourth Summer School in Analysis and Mathematical Physics

Topics in Spectral Theory and Quantum Mechanics, May 2005, Universidad Nacional Autónoma de México, Cuernavaca, Mexico

Author: Carlos Villegas-Blas

Publisher: American Mathematical Soc.

ISBN: 0821840649

Category: Mathematics

Page: 148

View: 4587

This book consists of three expository articles written by outstanding researchers in Mathematical Physics: Rafael Benguria, Peter Hislop, and Elliott Lieb. The articles are based on their lectures at the Fourth Summer School in Analysis and Mathematical Physics, held at the Institute of Mathematics, Universidad Nacional Autonoma de Mexico, Cuernavaca in May 2005. The main goal of the articles is to link the basic knowledge of a graduate student in Mathematics with three current research topics in Mathematical Physics: Isoperimetric inequalities for eigenvalues of the Laplace Operator, Random Schrodinger Operators, and Stability of Matter, respectively. These well written articles will guide and introduce the reader to current research topics and will also provide information on recent progress in some areas of Mathematical Physics.

Topics in Contemporary Differential Geometry, Complex Analysis and Mathematical Physics

Proceedings of the 8th International Workshop on Complex Structures and Vector Fields, Institute of Mathematics and Informatics, Bulgaria, 21-26 August 2006

Author: Stancho Dimiev,Kouei Sekigawa

Publisher: World Scientific

ISBN: 9812707905

Category: Mathematics

Page: 335

View: 4114

This volume contains the contributions by the participants in the eight of a series workshops in complex analysis, differential geometry and mathematical physics and related areas.Active specialists in mathematical physics contribute to the volume, providing not only significant information for researchers in the area but also interesting mathematics for non-specialists and a broader audience. The contributions treat topics including differential geometry, partial differential equations, integrable systems and mathematical physics.

Second Summer School in Analysis and Mathematical Physics

Topics in Analysis : Harmonic, Complex, Nonlinear, and Quantization : Second Summer School in Analysis and Mathematical Physics, Cuernavaca Morelos, Mexico, June 12-22, 2000

Author: m Summer School in Analysis and Mathematical Physics 2000 Cuernavaca,Salvador Pérez-Esteva,Carlos Villegas-Blas,Summer School in Analysis and Mathematical Physics

Publisher: American Mathematical Soc.

ISBN: 0821827081

Category: Mathematics

Page: 272

View: 421

For the second time, a Summer School in Analysis and Mathematical Physics took place at the Universidad Nacional Autonoma de Mexico in Cuernavaca. The purpose of the schools is to provide a bridge from standard graduate courses in mathematics to current research topics, particularly in analysis. The lectures are given by internationally recognized specialists in the fields. The topics covered in this Second Summer School include harmonic analysis, complex analysis, pseudodifferential operators, the mathematics of quantum chaos, and non-linear analysis.

Second Summer School in Analysis and Mathematical Physics

Topics in Analysis : Harmonic, Complex, Nonlinear, and Quantization : Second Summer School in Analysis and Mathematical Physics, Cuernavaca Morelos, Mexico, June 12-22, 2000

Author: Salvador Pérez-Esteva,Carlos Villegas-Blas

Publisher: American Mathematical Soc.

ISBN: 9780821856253

Category: Mathematics

Page: 272

View: 3349

For the second time, a Summer School in Analysis and Mathematical Physics took place at the Universidad Nacional Autonoma de Mexico in Cuernavaca. The purpose of the schools is to provide a bridge from standard graduate courses in mathematics to current research topics, particularly in analysis. The lectures are given by internationally recognized specialists in the fields. The topics covered in this Second Summer School include harmonic analysis, complex analysis, pseudodifferential operators, the mathematics of quantum chaos, and non-linear analysis.

Recent Advances in Differential Equations and Mathematical Physics

UAB International Conference on Differential Equations and Mathematical Physics, March 29-April 2, 2005, University of Alabama at Birmingham

Author: Nikolai Chernov

Publisher: American Mathematical Soc.

ISBN: 0821838407

Category: Mathematics

Page: 333

View: 2408

This book brings together both new material and recent surveys on some topics in differential equations that are either directly relevant to, or closely associated with, mathematical physics. Its topics include asymptotic formulas for the ground-state energy of fermionic gas, renormalization ideas in quantum field theory from perturbations of the free Hamiltonian on the circle, $J$-self adjoint Dirac operators, spectral theory of Schrodinger operators, inverse problems, isoperimetric inequalities in quantum mechanics, Hardy inequalities, and non-adiabatic transitions. Excellent survey articles on Dirichlet-Neumann inverse problems on manifolds (by Uhlmann), numerical investigations associated with Laplacian eigenvalues on planar regions (by Trefethen), Snell's law and propagation of singularities in the wave equation (by Vasy), and random operators on tree graphs (by Aizenmann) make this book interesting and valuable for graduate students, young mathematicians, and physicists alike.

Topics in Mathematical Physics, General Relativity, and Cosmology in Honor of Jerzy Pleba?ski

Proceedings of 2002 International Conference, Cinvestav, Mexico City, 17-20 September 2002

Author: Hugo Garc¡a-Compe n,Bogdan Mielnik,Merced Montesinos

Publisher: World Scientific

ISBN: 9812700471

Category: Science

Page: 513

View: 5376

One of modern science's most famous and controversial figures, Jerzy Plebanski was an outstanding theoretical physicist and an author of many intriguing discoveries in general relativity and quantum theory. Known for his exceptional analytic talents, explosive character, inexhaustible energy, and bohemian nights with brandy, coffee, and enormous amounts of cigarettes, he was dedicated to both science and art, producing innumerable handwritten articles - resembling monk's calligraphy - as well as a collection of oil paintings. As a collaborator but also an antagonist of Leopold Infeld's (a coauthor of Albert Einstein's), Plebanski is recognized for designing the "heavenly" and "hyper-heavenly" equations, for introducing new variables to describe the gravitational field, for the exact solutions in Einstein's gravity and in quantum theory, for his classification of the tensor of matter, for some outstanding results in nonlinear electrodynamics, and for analyzing general relativity with continuous sources long before Chandrasekhar et al. A tribute to Plebaski's contributions and the variety of his interests, this is a unique and wide-ranging collection of invited papers, covering gravity quantization, strings, branes, supersymmetry, ideas on the deformation quantization, and lesser known results on the continuous Baker-Campbell-Hausdorff problem.

Mathematical Physics

A Modern Introduction to Its Foundations

Author: Sadri Hassani

Publisher: Springer Science & Business Media

ISBN: 9780387985794

Category: Science

Page: 1026

View: 2131

For physics students interested in the mathematics they use, and for math students interested in seeing how some of the ideas of their discipline find realization in an applied setting. The presentation strikes a balance between formalism and application, between abstract and concrete. The interconnections among the various topics are clarified both by the use of vector spaces as a central unifying theme, recurring throughout the book, and by putting ideas into their historical context. Enough of the essential formalism is included to make the presentation self-contained.

Contemporary Mathematical Physics

F. A. Berezin Memorial Volume

Author: R. L. Dobrushin

Publisher: American Mathematical Soc.

ISBN: 9780821804261

Category: Mathematical physics

Page: 236

View: 9686

This two-volume collection is a celebration of the scientific heritage of F.A. Berezin (1931-1980). Before his untimely death, Berezin had an important influence on physics and mathematics, discovering new ideas in mathematical physics, representation theory, analysis, geometry, and other areas of mathematics. His crowning achievements were the introduction of a new notion of deformation quantization, and Grassmannian analysis (supermathematics). Collected here are papers by many of his colleagues and others who worked in related areas, representing a wide spectrum of topics in mathematical physics and allied areas of mathematics. In particular, the papers discuss quantization, invariant integration, spectral theory, and representation theory.

Topological and Algebraic Geometry Methods in Contemporary Mathematical Physics

Author: B. A. Dubrovin,I. M. Krichever,Sergeĭ Petrovich Novikov

Publisher: N.A

ISBN: 9781904868309

Category: Geometry, Algebraic

Page: 139

View: 6538

This volume is a classic survey of algebraic geometry and topological methods in various problems of mathematical physics and provides an excellent reference text for graduate students and researchers. The book is divided into three parts: the first part concerns Hamiltonian formalism and methods that generalise Morse for certain dynamical systems of physical origin; the second part presents algebraic geometry analysis of the Yang-Baxter equations for two-dimensional models; and finally, part three presents the theory of multidimensional theta functions of Abel, Riemann, Poincare in a form that is elementally and convenient for applications.

Perspectives in Mathematical Sciences

Author: Yisong Yang,Xinchu Fu,Jinqiao Duan

Publisher: World Scientific

ISBN: 9814289310

Category: Mathematics

Page: 354

View: 514

Mathematical sciences have been playing an increasingly important role in modern society. They are in high demand for investigating complex problems in physical science, environmental and geophysical sciences, materials science, life science and chemical sciences. This is a review volume on some timely and interesting topics in applied mathematical sciences. It reviews new developments and presents some future research directions in these topics. The chapters are written by reknowned experts in these fields. The volume is written with a wide audience in mind and hence will be accessible to graduate students, junior researchers and other professionals who are interested in the subject. The contributions of Professor Youzhong Guo, a leading expert in these areas, will be celebrated. An entire chapter will be devoted to his achievements. The underlying theme that binds the various chapters seamlessly is a set of dedicated ideas and techniques from partial differential equations and dynamical systems.

Wranglers and Physicists

Studies on Cambridge Physics in the Nineteenth Century

Author: Peter Michael Harman

Publisher: Manchester University Press

ISBN: 9780719017568

Category: Cambridge (England)

Page: 261

View: 4305


Applied Wave Mathematics

Selected Topics in Solids, Fluids, and Mathematical Methods

Author: Ewald Quak,Tarmo Soomere

Publisher: Springer Science & Business Media

ISBN: 3642005853

Category: Mathematics

Page: 471

View: 5105

This edited volume consists of twelve contributions related to the EU Marie Curie Transfer of Knowledge Project Cooperation of Estonian and Norwegian Scienti c Centres within Mathematics and its Applications, CENS-CMA (2005-2009), - der contract MTKD-CT-2004-013909, which ?nanced exchange visits to and from CENS, the Centre for Nonlinear Studies at the Institute of Cybernetics of Tallinn University of Technology in Estonia. Seven contributions describe research highlights of CENS members, two the work of members of CMA, the Centre of Mathematics for Applications,Univ- sity of Oslo, Norway, as the partner institution of CENS in the Marie Curie project, and three the ?eld of work of foreign research fellows, who visited CENS as part of theproject. Thestructureofthebookre?ectsthedistributionofthetopicsaddressed: Part I Waves in Solids Part II Mesoscopic Theory Part III Exploiting the Dissipation Inequality Part IV Waves in Fluids Part V Mathematical Methods The papers are written in a tutorial style, intended for non-specialist researchers and students, where the authors communicate their own experiences in tackling a problem that is currently of interest in the scienti?c community. The goal was to produce a book, which highlights the importance of applied mathematics and which can be used for educational purposes, such as material for a course or a seminar. To ensure the scienti?c quality of the contributions, each paper was carefully - viewed by two international experts. Special thanks go to all authors and referees, without whom making this book would not have been possible.

Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics

Author: Yuri E. Gliklikh

Publisher: Springer Science & Business Media

ISBN: 9401586349

Category: Mathematics

Page: 192

View: 5567

The geometrical methods in modem mathematical physics and the developments in Geometry and Global Analysis motivated by physical problems are being intensively worked out in contemporary mathematics. In particular, during the last decades a new branch of Global Analysis, Stochastic Differential Geometry, was formed to meet the needs of Mathematical Physics. It deals with a lot of various second order differential equations on finite and infinite-dimensional manifolds arising in Physics, and its validity is based on the deep inter-relation between modem Differential Geometry and certain parts of the Theory of Stochastic Processes, discovered not so long ago. The foundation of our topic is presented in the contemporary mathematical literature by a lot of publications devoted to certain parts of the above-mentioned themes and connected with the scope of material of this book. There exist some monographs on Stochastic Differential Equations on Manifolds (e. g. [9,36,38,87]) based on the Stratonovich approach. In [7] there is a detailed description of It6 equations on manifolds in Belopolskaya-Dalecky form. Nelson's book [94] deals with Stochastic Mechanics and mean derivatives on Riemannian Manifolds. The books and survey papers on the Lagrange approach to Hydrodynamics [2,31,73,88], etc. , give good presentations of the use of infinite-dimensional ordinary differential geometry in ideal hydrodynamics. We should also refer here to [89,102], to the previous books by the author [53,64], and to many others.

Proceedings of the Third International Workshop on Contemporary Problems in Mathematical Physics

Cotonou, Republic of Benin, 1-7 November 2003

Author: Jan Govaerts

Publisher: World Scientific

ISBN: 9789812702487

Category: Electronic books

Page: 628

View: 630

The COPROMAPH Conference series has now evolved into a significant international arena where fundamental concepts in mathematical and theoretical physics and their physics applications can be conceived, developed and disseminated. Basic ideas for addressing a variety of contemporary problems in mathematical and theoretical physics are presented in a nonintimidating atmosphere. Experts provide the reader the fundamentals to predict new possibilities in physics and other fields.The proceedings have been selected for coverage in: OCo Index to Scientific & Technical Proceedings- (ISTP- / ISI Proceedings)OCo Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)OCo CC Proceedings OCo Engineering & Physical Sciences"

Topics in Contemporary Mathematics

Author: Ignacio Bello,Jack Rolf Britton

Publisher: Houghton Mifflin College Division

ISBN: 9780618054602

Category: Mathematics

Page: 905

View: 8546

Topics in Contemporary Mathematics, 8/e, is uniquely designed to help students see math at work in the contemporary world by presenting problem solving in purposeful and meaningful contexts.

Pseudoperiodic Topology

Author: Maxim Kontsevich

Publisher: American Mathematical Soc.

ISBN: 9780821820940

Category: Mathematics

Page: 178

View: 2207

This volume offers an account of the present state of the art in pseudoperiodic topology - a young branch of mathematics, born at the boundary between the ergodic theory of dynamical systems, topology, and number theory. Related topics include the theory of algorithms, convex integer polyhedra, Morse inequalities, real algebraic geometry, statistical physics, and algebraic number theory. The book contains many new results. Most of the articles contain brief surveys on the topics, making the volume accessible to a broad audience. From the Preface by V.I. Arnold: 'The authors...have done much to show how modern mathematics begets, from this sea of pathological counterexamples, remarkable general and universal laws, whose discovery would be unthinkable and whose formulation would be impossible in the naive set-theoretical setting'.

Introduction to Mathematical Physics

Author: Michael T. Vaughn

Publisher: John Wiley & Sons

ISBN: 3527618864

Category: Science

Page: 543

View: 1567

A comprehensive survey of all the mathematical methods that should be available to graduate students in physics. In addition to the usual topics of analysis, such as infinite series, functions of a complex variable and some differential equations as well as linear vector spaces, this book includes a more extensive discussion of group theory than can be found in other current textbooks. The main feature of this textbook is its extensive treatment of geometrical methods as applied to physics. With its introduction of differentiable manifolds and a discussion of vectors and forms on such manifolds as part of a first-year graduate course in mathematical methods, the text allows students to grasp at an early stage the contemporary literature on dynamical systems, solitons and related topological solutions to field equations, gauge theories, gravitational theory, and even string theory. Free solutions manual available for lecturers at www.wiley-vch.de/supplements/.