Topics In Contemporary Mathematical Physics

Author : Kai S Lam
Publisher : World Scientific Publishing Company
Page : 852 pages
File Size : 41,6 Mb
Release : 2015-09-17
Category : Science
ISBN : 9789814667821

Get Book

Topics in Contemporary Mathematical Physics by Kai S Lam Pdf

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.

Author : Kai S Lam
Publisher : World Scientific Publishing Company
Page : 620 pages
File Size : 49,5 Mb
Release : 2003-06-06
Category : Science
ISBN : 9789813102309

Get Book

Topics in Contemporary Mathematical Physics by Kai S Lam Pdf

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.

Author : Kai Shue Lam
Publisher : World Scientific
Page : 628 pages
File Size : 52,9 Mb
Release : 2003
Category : Science
ISBN : 9812384049

Get Book

Topics in Contemporary Mathematical Physics by Kai Shue Lam Pdf

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; and (3) topology and differential geometry. The features of this work include: an exposition style which is a fusion of those common in the standard physics and mathematics literatures; a level of exposition that varies from quite elementary to moderately advanced, so that the text should be of interest to a wide audience; a strong degree of thematic unity, despite the diversity of the topics covered; and cross references, so that, from any part of the book, the reader can trace easily where specific concepts or techniques are introduced.

Author : Kouei Sekigawa,Stancho Dimiev
Publisher : World Scientific
Page : 352 pages
File Size : 44,6 Mb
Release : 2007-06-11
Category : Mathematics
ISBN : 9789814475020

Get Book

Topics In Contemporary Differential Geometry, Complex Analysis And Mathematical Physics - Proceedings Of The 8th International Workshop On Complex Structures And Vector Fields by Kouei Sekigawa,Stancho Dimiev Pdf

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.

Author : Roman W. Jackiw
Publisher : World Scientific
Page : 528 pages
File Size : 51,8 Mb
Release : 1995
Category : Science
ISBN : 9810216971

Get Book

Diverse Topics in Theoretical and Mathematical Physics by Roman W. Jackiw Pdf

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.

Author : L. A. Bunimovich,B. M. Gurevich,Ya. B. Pesin
Publisher : American Mathematical Soc.
Page : 8 pages
File Size : 48,9 Mb
Release : 1996
Category : Differentiable dynamical systems
ISBN : 0821804561

Get Book

Sinai's Moscow Seminar on Dynamical Systems by L. A. Bunimovich,B. M. Gurevich,Ya. B. Pesin Pdf

Author : Jan Govaerts,M Norbert Hounkonnou,Alfred Z Msezane
Publisher : World Scientific
Page : 504 pages
File Size : 41,8 Mb
Release : 2002-10-18
Category : Science
ISBN : 9789814488686

Get Book

Contemporary Problems in Mathematical Physics by Jan Govaerts,M Norbert Hounkonnou,Alfred Z Msezane Pdf

The following topics are discussed in this volume: recent developments in operator theory, coherent states and wavelet analysis, geometric and topological methods in theoretical physics and quantum field theory, and applications of these methods of mathematical physics to problems in atomic and molecular physics as well as the world of the elementary particles and their fundamental interactions. Two extensive sets of lecture notes on quantization techniques in general, and quantum gauge theories and strings as an avenue towards quantum geometry, are also included. The volume should be of interest to anyone working in a field using the mathematical methods associated with any of these topics. Contents:Quantization Techniques: A Quick Overview (S T Ali)The Quantum Geometer's Universe: Particles, Interactions and Topology (J Govaerts)Theoretical Methods of Modern Classical and Quantum Physics:Do Cross-Sections Determine Phase Shifts Uniquely? (D Atkinson)Hilbert Transform or Kramers-Kronig Relations Applied to Some Aspects of Linear and Nonlinear Physics (G Debiais)Application of the Gibbs Sampler to the Conditional Simulation of Rain Fields (H Onibon et al.)The Mathematics of an Algebraic Approach to the Physics of Hadrons (M D Slaughter)Coherent States, Wavelets and Geometric Methods in Theoretical Physics:Phase Space Geometry in Classical and Quantum Mechanics (J R Klauder)Functional Analysis Special Functions and Orthogonal Polynomials:On Generalized Continuous D Semi-Classical Hermite and Chebychev Orthogonal Polynomials of Class One (E Azatassou & M N Hounkonnou)On a Generalization of the Method by Barbaroux et al. for the Improvement on the Rate of Decay of an Operator Resolvent (G Honnouvo & M N Hounkonnou)and other papers Readership: Researchers in mathematical physics, theoretical physics, physical chemistry, analysis and differential equations, atomic and quantum physics. Keywords:

Author : Steeb Willi-hans
Publisher : World Scientific
Page : 736 pages
File Size : 48,5 Mb
Release : 2018-08-23
Category : Science
ISBN : 9789813275393

Get Book

Theoretical and Mathematical Physics by Steeb Willi-hans Pdf

This updated and extended edition of the book combines the topics provided in the two parts of the previous editions as well as new topics. It is a comprehensive compilation covering most areas in mathematical and theoretical physics. The book provides a collection of problems together with their detailed solutions which will prove to be valuable to students as well as to researchers in the fields of mathematics, physics, engineering and other sciences. Each chapter provides a short introduction with the relevant definitions and notations. All relevant definitions are given. The topics range in difficulty from elementary to advanced. Almost all problems are solved in detail and most of the problems are self-contained. Stimulating supplementary problems are also provided in each chapter. Students can learn important principles and strategies required for problem solving. Teachers will also find this text useful as a supplement, since important concepts and techniques are developed in the problems. Introductory problems for both undergraduate and advanced undergraduate students are provided. More advanced problems together with their detailed solutions are collected, to meet the needs of graduate students and researchers. Problems included cover new fields in theoretical and mathematical physics such as tensor product, Lax representation, Bäcklund transformation, soliton equations, Hilbert space theory, uncertainty relation, entanglement, spin systems, Lie groups, Bose system, Fermi systems differential forms, Lie algebra valued differential forms, metric tensor fields, Hirota technique, Painlevé test, Bethe ansatz, Yang-Baxter relation, wavelets, gauge theory, differential geometry, string theory, chaos, fractals, complexity, ergodic theory, etc. A number of software implementations are also provided.

Author : Ignacio Bello,Jack Rolf Britton
Publisher : Houghton Mifflin
Page : 0 pages
File Size : 52,9 Mb
Release : 2004-02
Category : Mathematics
ISBN : 0618347526

Get Book

Topics in Contemporary Mathematics by Ignacio Bello,Jack Rolf Britton Pdf

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.

Author : Marek Biskup,Anton Bovier,Frank den Hollander,Dima Ioffe,Fabio Martinelli,Karel Netocný,Christina Toninelli
Publisher : Springer
Page : 350 pages
File Size : 49,5 Mb
Release : 2009-07-31
Category : Mathematics
ISBN : 9783540927969

Get Book

Methods of Contemporary Mathematical Statistical Physics by Marek Biskup,Anton Bovier,Frank den Hollander,Dima Ioffe,Fabio Martinelli,Karel Netocný,Christina Toninelli Pdf

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. It presents new results on phase transitions for gradient lattice models.

Author : Peter Szekeres
Publisher : Cambridge University Press
Page : 620 pages
File Size : 45,8 Mb
Release : 2004-12-16
Category : Mathematics
ISBN : 0521829607

Get Book

A Course in Modern Mathematical Physics by Peter Szekeres Pdf

This textbook, first published in 2004, provides an introduction to the major mathematical structures used in physics today.

Author : Dorothea Bahns,Wolfram Bauer,Ingo Witt
Publisher : Birkhäuser
Page : 314 pages
File Size : 52,8 Mb
Release : 2016-02-11
Category : Mathematics
ISBN : 9783319224077

Get Book

Quantization, PDEs, and Geometry by Dorothea Bahns,Wolfram Bauer,Ingo Witt Pdf

This book presents four survey articles on different topics in mathematical analysis that are closely linked to concepts and applications in physics. Specifically, it discusses global aspects of elliptic PDEs, Berezin-Toeplitz quantization, the stability of solitary waves, and sub-Riemannian geometry. The contributions are based on lectures given by distinguished experts at a summer school in Göttingen. The authors explain fundamental concepts and ideas and present them clearly. Starting from basic notions, these course notes take the reader to the point of current research, highlighting new challenges and addressing unsolved problems at the interface between mathematics and physics. All contributions are of interest to researchers in the respective fields, but they are also accessible to graduate students.

Author : Sadri Hassani
Publisher : Springer Science & Business Media
Page : 680 pages
File Size : 55,9 Mb
Release : 2000-06-15
Category : Mathematics
ISBN : 0387989587

Get Book

Mathematical Methods by Sadri Hassani Pdf

Intended to follow the usual introductory physics courses, this book contains many original, lucid and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts to help guide students through the material.

Author : A Fokas,A Grigoryan,T Kibble,B Zegarlinski
Publisher : World Scientific
Page : 336 pages
File Size : 44,7 Mb
Release : 2000-05-05
Category : Science
ISBN : 9781783261710

Get Book

Mathematical Physics 2000 by A Fokas,A Grigoryan,T Kibble,B Zegarlinski Pdf

Mathematical physics has made enormous strides over the past few decades, with the emergence of many new disciplines and with revolutionary advances in old disciplines. One of the especially interesting features is the link between developments in mathematical physics and in pure mathematics. Many of the exciting advances in mathematics owe their origin to mathematical physics — superstring theory, for example, has led to remarkable progress in geometry — while very pure mathematics, such as number theory, has found unexpected applications. The beginning of a new millennium is an appropriate time to survey the present state of the field and look forward to likely advances in the future. In this book, leading experts give personal views on their subjects and on the wider field of mathematical physics. The topics covered range widely over the whole field, from quantum field theory to turbulence, from the classical three-body problem to non-equilibrium statistical mechanics. Contents: Modern Mathematical Physics: What It Should Be (L D Faddeev)New Applications of the Chiral Anomaly (J Fröhlich & B Pedrini)Fluctuations and Entropy Driven Space–Time Intermittency in Navier–Stokes Fluids (G Gallavotti)Superstrings and the Unification of the Physical Forces (M B Green)Questions in Quantum Physics: A Personal View (R Haag)What Good are Quantum Field Theory Infinities? (R Jackiw)Constructive Quantum Field Theory (A Jaffe)Fourier's Law: A Challenge to Theorists (F Bonetto et al.)The “Corpuscular” Structure of the Spectra of Operators Describing Large Systems (R A Minlos)Vortex- and Magneto-Dynamics — A Topological Perspective (H K Moffatt)Gauge Theory: The Gentle Revolution (L O'Raifeartaigh)Random Matrices as Paradigm (L Pastur)Wavefunction Collapse as a Real Gravitational Effect (R Penrose)Schrödinger Operators in the Twenty-First Century (B Simon)The Classical Three-Body Problem — Where is Abstract Mathematics, Physical Intuition, Computational Physics Most Powerful? (H A Posch & W Thirring)Infinite Particle Systems and Their Scaling Limits (S R S Varadhan)Supersymmetry: A Personal View (B Zumino) Readership: Mathematicians and physicists. Keywords:London (GB);Proceedings;Congress;Mathematical Physics

Author : I. S. Krasil′shchik,A. B. Sossinsky,A. M. Verbovetsky
Publisher : American Mathematical Society
Page : 250 pages
File Size : 52,9 Mb
Release : 2023-08-21
Category : Mathematics
ISBN : 9781470471477

Get Book

The Diverse World of PDEs by I. S. Krasil′shchik,A. B. Sossinsky,A. M. Verbovetsky Pdf

This volume contains the proceedings of the Alexandre Vinogradov Memorial Conference on Diffieties, Cohomological Physics, and Other Animals, held from December 13–17, 2021, at the Independent University of Moscow and Moscow State University, Moscow, Russia. The papers are devoted to various interrelations of nonlinear PDEs with geometry and integrable systems. The topics discussed are: gravitational and electromagnetic fields in General Relativity, nonlocal geometry of PDEs, Legendre foliated cocycles on contact manifolds, presymplectic gauge PDEs and Lagrangian BV formalism, jet geometry and high-order phase transitions, bi-Hamiltonian structures of KdV type, bundles of Weyl structures, Lax representations via twisted extensions of Lie algebras, energy functionals and normal forms of knots, and differential invariants of inviscid flows. The companion volume (Contemporary Mathematics, Volume 789) is devoted to Algebraic and Cohomological Aspects of PDEs.