Topics in Contemporary Mathematical Physics

Second Edition

Author: Kai S Lam

Publisher: World Scientific Publishing Company

ISBN: 981466782X

Category: Science

Page: 852

View: 7138

This new (second) edition contains a general treatment of quantum field theory (QFT) in a simple scalar field setting in addition to the modern material on the applications of differential geometry and topology, group theory, and the theory of linear operators to physics found in the first edition. All these are introduced without assuming more background on the part of the reader than a good foundation in undergraduate (junior) level mathematical physics. The new material entirely focuses on an introduction to quantum field theory, emphasizing the Feynman path (functional integral) approach to QFT and the renormalization group. With respect to the latter, the focus is on an introduction of its application to critical phenomena in statistical physics, following the outgrowth of the Callan–Symanzik equation originally developed in the context of high energy physics, and the seminal contributions of Kenneth Wilson. One of the overriding aims of the new material is also to draw students' attention to the deep connections between high energy physics and statistical mechanics. The unavoidable technical aspects are explained with a minimum of prerequisite material and jargon, and conceptual understanding is always given prominence before mastery of technical details, but the importance of the latter is never underestimated. Derivational details and motivational discussions are provided in abundance in order to ensure continuity of reading, and to avoid trying the readers' patience.

Diverse Topics in Theoretical and Mathematical Physics

Author: Roman W. Jackiw

Publisher: World Scientific

ISBN: 9789810216979

Category: Science

Page: 514

View: 8472

In this volume, topics are drawn from field theory, especially gauge field theory, as applied to particle, condensed matter and gravitational physics, and concern a variety of interesting subjects. These include geometricalDtopological effects in quantum theory, fractional charge, time travel, relativistic quantized fields in and out of thermal equilibrium and quantum modifications of symmetry in physical systems.Many readers will find this a useful volume, especially theoretical physicists and mathematicians. The material will be of interest to both the expert who will find well-presented novel and stimulating viewpoints of various subjects and the novice who will find complete, detailed and precise descriptions of important topics of current interest, in theoretical 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: Salvador Pérez-Esteva,Carlos Villegas-Blas

Publisher: American Mathematical Soc.

ISBN: 0821827081

Category: Mathematics

Page: 272

View: 3970

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.

Topics in Contemporary Mathematics

Author: Ignacio Bello,Anton Kaul,Jack R. Britton

Publisher: Cengage Learning

ISBN: 1133107427

Category: Mathematics

Page: 992

View: 4590

Written for the Math for Liberal Arts course, TOPICS IN CONTEMPORARY MATHEMATICS helps students see math at work in the world by presenting problem solving in purposeful and meaningful contexts. Many of the problems in the text demonstrate how math relates to subjects--such as sociology, psychology, business, and technology--that generally interest students. Available with InfoTrac Student Collections http://gocengage.com/infotrac. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Mathematical Physics

Author: Robert Geroch

Publisher: University of Chicago Press

ISBN: 022622306X

Category: Science

Page: 358

View: 7748

Mathematical Physics is an introduction to such basic mathematical structures as groups, vector spaces, topological spaces, measure spaces, and Hilbert space. Geroch uses category theory to emphasize both the interrelationships among different structures and the unity of mathematics. Perhaps the most valuable feature of the book is the illuminating intuitive discussion of the "whys" of proofs and of axioms and definitions. This book, based on Geroch's University of Chicago course, will be especially helpful to those working in theoretical physics, including such areas as relativity, particle physics, and astrophysics.

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

Publisher: World Scientific

ISBN: 9812709800

Category: Mathematics

Page: 350

View: 9480

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.

Physical Mathematics

Author: Kevin Cahill

Publisher: Cambridge University Press

ISBN: 1107310733

Category: Science

Page: N.A

View: 5448

Unique in its clarity, examples and range, Physical Mathematics explains as simply as possible the mathematics that graduate students and professional physicists need in their courses and research. The author illustrates the mathematics with numerous physical examples drawn from contemporary research. In addition to basic subjects such as linear algebra, Fourier analysis, complex variables, differential equations and Bessel functions, this textbook covers topics such as the singular-value decomposition, Lie algebras, the tensors and forms of general relativity, the central limit theorem and Kolmogorov test of statistics, the Monte Carlo methods of experimental and theoretical physics, the renormalization group of condensed-matter physics and the functional derivatives and Feynman path integrals of quantum field theory.

Mathematics for Physics

A Guided Tour for Graduate Students

Author: Michael Stone,Paul Goldbart

Publisher: Cambridge University Press

ISBN: 1139480618

Category: Science

Page: N.A

View: 3548

An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of physics – differential and integral equations, Fourier series and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and complex variables. The authors' exposition avoids excess rigor whilst explaining subtle but important points often glossed over in more elementary texts. The topics are illustrated at every stage by carefully chosen examples, exercises and problems drawn from realistic physics settings. These make it useful both as a textbook in advanced courses and for self-study. Password-protected solutions to the exercises are available to instructors at www.cambridge.org/9780521854030.

Contemporary Mathematical Physics

F. A. Berezin Memorial Volume

Author: R. L. Dobrushin

Publisher: American Mathematical Soc.

ISBN: 9780821804261

Category: Mathematical physics

Page: 236

View: 7625

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.

Non-Relativistic Quantum Theory

Dynamics, Symmetry, and Geometry

Author: Kai S Lam

Publisher: World Scientific Publishing Company

ISBN: 9813107480

Category: Science

Page: 460

View: 3855

This textbook is mainly for physics students at the advanced undergraduate and beginning graduate levels, especially those with a theoretical inclination. Its chief purpose is to give a systematic introduction to the main ingredients of the fundamentals of quantum theory, with special emphasis on those aspects of group theory (spacetime and permutational symmetries and group representations) and differential geometry (geometrical phases, topological quantum numbers, and Chern–Simons Theory) that are relevant in modern developments of the subject. It will provide students with an overview of key elements of the theory, as well as a solid preparation in calculational techniques.

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: 0821827081

Category: Mathematics

Page: 272

View: 9956

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.

A Course in Modern Mathematical Physics

Groups, Hilbert Space and Differential Geometry

Author: Peter Szekeres

Publisher: Cambridge University Press

ISBN: 9780521829601

Category: Mathematics

Page: 600

View: 6976

This book provides an introduction to the mathematics of modern physics, presenting concepts and techniques in mathematical physics at a level suitable for advanced undergraduates and beginning graduate students. It aims to introduce the reader to modern mathematical thinking within a physics setting. Topics covered include tensor algebra, differential geometry, topology, Lie groups and Lie algebras, distribution theory, fundamental analysis and Hilbert spaces. The book includes exercises and worked examples, to test the students' understanding of the various concepts, as well as extending the themes covered in the main text.

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: 4803

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.

Introduction to Mathematical Physics

Author: Michael T. Vaughn

Publisher: John Wiley & Sons

ISBN: 3527618864

Category: Science

Page: 543

View: 2235

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/.

Mathematics of Classical and Quantum Physics

Author: Frederick W. Byron,Robert W. Fuller

Publisher: Courier Corporation

ISBN: 0486135063

Category: Science

Page: 672

View: 3463

Graduate-level text offers unified treatment of mathematics applicable to many branches of physics. Theory of vector spaces, analytic function theory, theory of integral equations, group theory, and more. Many problems. Bibliography.

Mathematical Methods Using Mathematica®

For Students of Physics and Related Fields

Author: Sadri Hassani

Publisher: Springer Science & Business Media

ISBN: 038721559X

Category: Science

Page: 235

View: 7513

Intended as a companion for textbooks in mathematical methods for science and engineering, this book presents a large number of numerical topics and exercises together with discussions of methods for solving such problems using Mathematica(R). Although it is primarily designed for use with the author's "Mathematical Methods: For Students of Physics and Related Fields," the discussions in the book sufficiently self-contained that the book can be used as a supplement to any of the standard textbooks in mathematical methods for undergraduate students of physical sciences or engineering.

Analysis, Complex Geometry, and Mathematical Physics

In Honor of Duong H. Phong

Author: Paul M. N. Feehan,Jian Song, Ben Weinkove,Richard A. Wentworth

Publisher: American Mathematical Soc.

ISBN: 1470414643

Category: Geometry, Differential

Page: 359

View: 3417

This volume contains the proceedings of the Conference on Analysis, Complex Geometry and Mathematical Physics: In Honor of Duong H. Phong, which was held from May 7-11, 2013, at Columbia University, New York. The conference featured thirty speakers who spoke on a range of topics reflecting the breadth and depth of the research interests of Duong H. Phong on the occasion of his sixtieth birthday. A common thread, familiar from Phong's own work, was the focus on the interplay between the deep tools of analysis and the rich structures of geometry and physics. Papers included in this volume cover topics such as the complex Monge-Ampère equation, pluripotential theory, geometric partial differential equations, theories of integral operators, integrable systems and perturbative superstring theory.

Methods of Contemporary Mathematical Statistical Physics

Author: Marek Biskup,Anton Bovier,Roman Kotecký

Publisher: Springer Science & Business Media

ISBN: 3540927956

Category: Mathematics

Page: 343

View: 1059

This volume presents a collection of courses introducing the reader to the recent progress with attention being paid to laying solid grounds and developing various basic tools. An introductory chapter on lattice spin models is useful as a background for other lectures of the collection. The topics include new results on phase transitions for gradient lattice models (with introduction to the techniques of the reflection positivity), stochastic geometry reformulation of classical and quantum Ising models, the localization/delocalization transition for directed polymers. A general rigorous framework for theory of metastability is presented and particular applications in the context of Glauber and Kawasaki dynamics of lattice models are discussed. A pedagogical account of several recently discussed topics in nonequilibrium statistical mechanics with an emphasis on general principles is followed by a discussion of kinetically constrained spin models that are reflecting important peculiar features of glassy dynamics.