Mathematical Physics 2000

Mathematical Physics 2000
Author: Athanassios Fokas
Publisher: World Scientific
Total Pages: 336
Release: 2000-05-05
Genre: Science
ISBN: 1783261714
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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.

Mathematical Physics 2000

Mathematical Physics 2000
Author: A. S. Fokas
Publisher: World Scientific Publishing Company
Total Pages: 326
Release: 2000-01-01
Genre: Mathematics
ISBN: 9781860942303
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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.

The Functions of Mathematical Physics

The Functions of Mathematical Physics
Author: Harry Hochstadt
Publisher: Courier Corporation
Total Pages: 354
Release: 2012-04-30
Genre: Science
ISBN: 0486168786
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A modern classic, this clearly written, incisive textbook provides a comprehensive, detailed survey of the functions of mathematical physics, a field of study straddling the somewhat artificial boundary between pure and applied mathematics. In the 18th and 19th centuries, the theorists who devoted themselves to this field — pioneers such as Gauss, Euler, Fourier, Legendre, and Bessel — were searching for mathematical solutions to physical problems. Today, although most of the functions have practical applications, in areas ranging from the quantum-theoretical model of the atom to the vibrating membrane, some, such as those related to the theory of discontinuous groups, still remain of purely mathematical interest. Chapters One and Two examine orthogonal polynomials, with sections on such topics as the recurrence formula, the Christoffel-Darboux formula, the Weierstrass approximation theorem, and the application of Hermite polynomials to quantum mechanics. Chapter Three is devoted to the principal properties of the gamma function, including asymptotic expansions and Mellin-Barnes integrals. Chapter Four covers hypergeometric functions, including a review of linear differential equations with regular singular points, and a general method for finding integral representations. Chapters Five and Six are concerned with the Legendre functions and their use in the solutions of Laplace's equation in spherical coordinates, as well as problems in an n-dimension setting. Chapter Seven deals with confluent hypergeometric functions, and Chapter Eight examines, at length, the most important of these — the Bessel functions. Chapter Nine covers Hill's equations, including the expansion theorems.

Methods of Mathematical Physics

Methods of Mathematical Physics
Author: Harold Jeffreys
Publisher: Cambridge University Press
Total Pages: 734
Release: 1999-11-18
Genre: Mathematics
ISBN: 9780521664028
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This book is a reissue of classic textbook of mathematical methods.

XIVth International Congress on Mathematical Physics

XIVth International Congress on Mathematical Physics
Author: Jean-Claude Zambrini
Publisher: World Scientific
Total Pages: 720
Release: 2005
Genre: Mathematics
ISBN: 981256201X
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In 2003 the XIV International Congress on Mathematical Physics (ICMP) was held in Lisbon with more than 500 participants. Twelve plenary talks were given in various fields of Mathematical Physics: E Carlen On the relation between the Master equation and the Boltzmann Equation in Kinetic Theory; A Chenciner Symmetries and "simple" solutions of the classical n-body problem; M J Esteban Relativistic models in atomic and molecular physics; K Fredenhagen Locally covariant quantum field theory; K Gawedzki Simple models of turbulent transport; I Krichever Algebraic versus Liouville integrability of the soliton systems; R V Moody Long-range order and diffraction in mathematical quasicrystals; S Smirnov Critical percolation and conformal invariance; J P Solovej The energy of charged matter; V Schomerus Strings through the microscope; C Villani Entropy production and convergence to equilibrium for the Boltzmann equation; D Voiculescu Aspects of free probability. ICMP 2003 also included invited talks by: H Eliasson, W Schlag, M Shub, P Dorey, J M Maillet, K McLaughlin, A Nakayashiki, A Okounkov, G M Graf, R Seiringer, S Teufel, J Imbrie, D Ioffe, H Knoerrer, D Bernard, J Dimock, C J Fewster, T Thiemann, F Benatti, D Evans, Y Kawahigashi, C King, B Julia, N Nekrasov, P Townsend, D Bambusi, M Hairer, V Kaloshin, G Schneider, A Shirikyan, P Bizon, H Bray, H Ringstrom, L Barreira, L Rey-Bellet, C Forster, P Gaspard, F Golse, T Chen, P Exner, T Ichinose, V Kostrykin, E Skibsted, G Stolz, D Yafaev, V A Zagrebnov, R Leandre, T Levy, S Mazzuchi, H Owhadi, M Roeckner and A Sengupta. Key Features Provides a list of the most recent progress in all fields of Mathematical Physics; Written by the best international experts in these fields; Indicates the "hot" directions of research in Mathematical Physics for years to come; Readership: Mathematical physicists, mathematicians and theoretical physicists.

Fifty Years of Mathematical Physics

Fifty Years of Mathematical Physics
Author: Molin Ge
Publisher: World Scientific Publishing Company
Total Pages: 596
Release: 2016-02-16
Genre: Science
ISBN: 9814340960
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This unique volume summarizes with a historical perspective several of the major scientific achievements of Ludwig Faddeev, with a foreword by Nobel Laureate C N Yang. The volume that spans over fifty years of Faddeev's career begins where he started his own scientific research, in the subject of scattering theory and the three-body problem. It then continues to describe Faddeev's contributions to automorphic functions, followed by an extensive account of his many fundamental contributions to quantum field theory including his original article on ghosts with Popov. Faddeev's contributions to soliton theory and integrable models are then described, followed by a survey of his work on quantum groups. The final scientific section is devoted to Faddeev's contemporary research including articles on his long-term interest in constructing knotted solitons and understanding confinement. The volume concludes with his personal view on science and mathematical physics in particular.

Clifford Algebras and their Applications in Mathematical Physics

Clifford Algebras and their Applications in Mathematical Physics
Author: Rafał Abłamowicz
Publisher: Springer Science & Business Media
Total Pages: 500
Release: 2000
Genre: Mathematics
ISBN: 9780817641825
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The first part of a two-volume set concerning the field of Clifford (geometric) algebra, this work consists of thematically organized chapters that provide a broad overview of cutting-edge topics in mathematical physics and the physical applications of Clifford algebras. algebras and their applications in physics. Algebraic geometry, cohomology, non-communicative spaces, q-deformations and the related quantum groups, and projective geometry provide the basis for algebraic topics covered. Physical applications and extensions of physical theories such as the theory of quaternionic spin, a projective theory of hadron transformation laws, and electron scattering are also presented, showing the broad applicability of Clifford geometric algebras in solving physical problems. Treatment of the structure theory of quantum Clifford algebras, the connection to logic, group representations, and computational techniques including symbolic calculations and theorem proving rounds out the presentation.

Mathematical Methods for Physicists

Mathematical Methods for Physicists
Author: Tai L. Chow
Publisher: Cambridge University Press
Total Pages: 575
Release: 2000-07-27
Genre: Science
ISBN: 1139427962
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This text is designed for an intermediate-level, two-semester undergraduate course in mathematical physics. It provides an accessible account of most of the current, important mathematical tools required in physics these days. It is assumed that the reader has an adequate preparation in general physics and calculus. The book bridges the gap between an introductory physics course and more advanced courses in classical mechanics, electricity and magnetism, quantum mechanics, and thermal and statistical physics. The text contains a large number of worked examples to illustrate the mathematical techniques developed and to show their relevance to physics. The book is designed primarily for undergraduate physics majors, but could also be used by students in other subjects, such as engineering, astronomy and mathematics.

Mathematical Analysis of Physical Problems

Mathematical Analysis of Physical Problems
Author: Philip Russell Wallace
Publisher:
Total Pages: 616
Release: 1972
Genre: Mathematical physics
ISBN: 9780080856261
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This mathematical reference for theoretical physics employs common techniques and concepts to link classical and modern physics. It provides the necessary mathematics to solve most of the problems. Topics include the vibrating string, linear vector spaces, the potential equation, problems of diffusion and attenuation, probability and stochastic processes, and much more.

Equations of Mathematical Physics

Equations of Mathematical Physics
Author: A. N. Tikhonov
Publisher: Courier Corporation
Total Pages: 802
Release: 2013-09-16
Genre: Mathematics
ISBN: 0486173364
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Mathematical physics plays an important role in the study of many physical processes — hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced undergraduate- or graduate-level text considers only those problems leading to partial differential equations. Contents: I. Classification of Partial Differential Equations II. Evaluations of the Hyperbolic Type III. Equations of the Parabolic Type IV. Equations of Elliptic Type V. Wave Propagation in Space VI. Heat Conduction in Space VII. Equations of Elliptic Type (Continuation) The authors — two well-known Russian mathematicians — have focused on typical physical processes and the principal types of equations dealing with them. Special attention is paid throughout to mathematical formulation, rigorous solutions, and physical interpretation of the results obtained. Carefully chosen problems designed to promote technical skills are contained in each chapter, along with extremely useful appendixes that supply applications of solution methods described in the main text. At the end of the book, a helpful supplement discusses special functions, including spherical and cylindrical functions.