Theodore Frankel

The Geometry of Physics
An Introduction, 2nd Edition

Publication is planned for March 2004 | Hardback | 720 pages 120 line diagrams | ISBN: 0-521-83330-2
Publication is planned for March 2004 | Paperback | 720 pages 120 line diagrams | ISBN: 0-521-53927-7

This book provides a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Included are discussions of analytical and fluid dynamics, electromagnetism (in flat and curved space), thermodynamics, the deformation tensors of elasticity, soap films, special and general relativity, the Dirac operator and spinors, and gauge fields, including Yang-Mills, the Aharonov-Bohm effect, Berry phase, and instanton winding numbers, quarks, and quark model for mesons. Before discussing abstract notions of differential geometry, geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space; consequently, the book should be of interest also to mathematics students. Ideal for graduate and advanced undergraduate students of physics, engineering and mathematics as a course text or for self study.

Contents

Preface; Part I. Manifolds, Tensors and Exterior Forms: 1. Manifolds and vector fields; 2. Tensors and exterior forms; 3. Integration of differential forms; 4. The Lie derivative; 5. The Poincare lemma and potentials; 6. Holonomic and non-holonomic constraints; Part II. Geometry and Topology: 7. R3 and Minkowski space; 8. The geometry of surfaces in R3; 9. Covariant differentiation and curvature; 10. Geodesics; 11. Relativity, tensors, and curvature; 12. Curvature and topology: Synge’s theorem; 13. Betti numbers and de Rham’s theorem; 14. Harmonic forms; Part III. Lie Groups, Bundles and Chern Forms: 15. Lie groups; 16. Vector bundles in geometry and physics; 17. Fiber bundles, Gauss-Bonnet, and topological quantization; 18. Connections and associated bundles; 19. The Dirac equation; 20. Yang-Mills fields; 21. Betti numbers and covering spaces; 22. Chern forms and homotopy groups; Appendix A. Forms in continuum mechanics; Appendix B. Harmonic chains and Kirchhoff’s circuit laws; Appendix C. Symmetries, quarks, and meson masses; Appendix D. Representations and hyperelastic bodies; Appendix E: Orbits and Morse-Bott theory in compact Lie groups.

Michel Le Bellac, Fabrice Mortessagne, George Batrouni

Equilibrium and Non-Equilibrium Statistical Thermodynamics

Publication is planned for April 2004 | Hardback | 628 pages 154 line diagrams 10 tables | ISBN: 0-521-82143-6

This graduate-level text gives a self-contained exposition of fundamental topics in modern equilibrium and nonequilibrium statistical thermodynamics. The text follows a balanced approach between the macroscopic (thermodynamic) and microscopic (statistical) points of view. The first half of the book deals with equilibrium thermodynamics and statistical mechanics. In addition to standard subjects, the reader will find a detailed account of broken symmetries, critical phenomena and the renormalization group, as well as an introduction to numerical methods. The second half of the book is devoted to nonequilibrium phenomena, first following a macroscopic approach, with hydrodynamics as an important example. Kinetic theory receives a thorough treatment through analysis of the Boltzmann-Lorentz model and the Boltzmann equation. The book concludes with general nonequilibrium methods such as linear response, projection method and the Langevin and Fokker-Planck equations, including numerical simulations. This advanced textbook will be of interest to graduate students and researchers in physics.

Contents

Preface; 1. Thermodynamics; 2. Statistical entropy and Boltzmann distribution; 3. Canonical and grand-canonical ensembles; 4. Critical phenomena; 5. Quantum statistics; 6. Irreversible processes: macroscopic theory; 7. Numerical simulations; 8. Irreversible processes: kinetic theory; 9. Topics in non-equilibrium statistical mechanics; 10. Appendices.

Edited by J. C. van den Berg

Wavelets in Physics

March 2004 | Paperback | 475 pages 76 line diagrams 42 half-tones 3 tables | ISBN: 0-521-53353-8

This book surveys the application of the recently developed technique of the wavelet transform to a wide range of physical fields, including astrophysics, turbulence, meteorology, plasma physics, atomic and solid state physics, multifractals occurring in physics, biophysics (in medicine and physiology) and mathematical physics. The wavelet transform can analyze scale-dependent characteristics of a signal (or image) locally, unlike the Fourier transform, and more flexibly than the windowed Fourier transform developed by Gabor fifty years ago. The continuous wavelet transform is used mostly for analysis, but the discrete wavelet transform allows very fast compression and transmission of data and speeds up numerical calculation, and is applied, for example, in the solution of partial differential equations in physics. This book will be of interest to graduate students and researchers in many fields of physics, and to applied mathematicians and engineers interested in physical application.

Contributors
J. C. van den Berg, J.-P. Antoine, A. Bijaoui, M. Farge, N. K.-R. Kevlahan, V. Perrier, K. Schneider, L. Hudgins, J. H. Kaspersen, B. Ph. van Milligen, A. Fournier, Ph. Antoine, B. Piraux, A. Arneodo, E. Bacry, J. F. Muzy, P. Ch. Ivanov, A. L. Goldberger, S. Havlin, C. -K. Peng, M. G. Rosenblum, H. E. Stanley, Ch.-A. Guerin, M. Holschneider

Contents

A guided tour J. C. van den Berg; 1. Wavelet analysis, a new tool in physics J.-P. Antoine; 2. The 2-D wavelet transform, physical applications J.-P. Antoine; 3. Wavelets and astrophysical applications A. Bijaoui; 4. Turbulence analysis, modelling and computing using wavelets M. Farge, N. K.-R. Kevlahan, V. Perrier and K. Schneider; 5. Wavelets and detection of coherent structures in fluid turbulence L. Hudgins and J. H. Kaspersen; 6. Wavelets, non-linearity and turbulence in fusion plasmas B. Ph. van Milligen; 7. Transfers and fluxes of wind kinetic energy between orthogonal wavelet components during atmospheric blocking A. Fournier; 8. Wavelets in atomic physics and in solid state physics J.-P. Antoine, Ph. Antoine and B. Piraux; 9. The thermodynamics of fractals revisited with wavelets A. Arneodo, E. Bacry and J. F. Muzy; 10. Wavelets in medicine and physiology P. Ch. Ivanov, A. L. Goldberger, S. Havlin, C.-K. Peng, M. G. Rosenblum and H. E. Stanley; 11. Wavelet dimension and time evolution Ch.-A. Guerin and M. Holschneider.

Abdelhak Zoubir, D. Robert Iskander

Bootstrap Techniques for Signal Processing

Publication is planned for April 2004 | Hardback | 228 pages 41 line diagrams 34 tables | ISBN: 0-521-83127-X

The statistical bootstrap is one of the methods that can be used to calculate estimates of a certain number of unknown parameters of a random process or a signal observed in noise, based on a random sample. Such situations are common in signal processing and the bootstrap is especially useful when only a small sample is available or an analytical analysis is too cumbersome or even impossible. This book covers the foundations of the bootstrap, its properties, its strengths, and its limitations. The authors focus on bootstrap signal detection in Gaussian and non-Gaussian interference as well as bootstrap model selection. The theory developed in the book is supported by a number of useful practical examples written in MATLAB. The book is aimed at graduate students and engineers, and includes applications to real-world problems in areas such as radar and sonar, biomedical engineering, and automotive engineering.

Contents

1. Introduction; 2. The bootstrap principle; 3. Signal detection with the bootstrap; 4. Bootstrap model selection; 5. Real data applications; Appendices.

Marc Cabanes, Michel Enguehard

Representation Theory of Finite Reductive Groups

New Series : New Mathematical Monographs

January 2004 | Hardback | 454 pages 144 exercises | ISBN: 0-521-82517-2

At the crossroads of representation theory, algebraic geometry and finite group theory, this book blends together many of the main concerns of modern algebra, synthesising the past 25 years of research, with full proofs of some of the most remarkable achievements in the area. Cabanes and Enguehard follow three main themes: first, applications of etale cohomology, leading to the proof of the recent Bonnafe?Rouquier theorems. The second is a straightforward and simplified account of the Dipper?James theorems relating irreducible characters and modular representations. The final theme is local representation theory. One of the main results here is the authors’ version of Fong?Srinivasan theorems. Throughout the text is illustrated by many examples and background is provided by several introductory chapters on basic results and appendices on algebraic geometry and derived categories. The result is an essential introduction for graduate students and reference for all algebraists.

Contents

Introduction; Notations and conventions; Part I. Representing Finite BN-Pairs: 1. Cuspidality in finite groups; 2. Finite BN-pairs; 3. Modular Hecke algebras for finite BN-pairs; 4. Modular duality functor and the derived category; 5. Local methods for the transversal characteristics; 6. Simple modules in the natural characteristic; Part II. Deligne?Lusztig Varieties, Rational Series, and Morita Equivalences: 7. Finite reductive groups and Deligne?Lusztig varieties; 8. Characters of finite reductive groups; 9. Blocks of finite reductive groups and rational series; 10. Jordan decomposition as a Morita equivalence, the main reductions; 11. Jordan decomposition as a Morita equivalence, sheaves; 12. Jordan decomposition as a Morita equivalence, modules; Part III. Unipotent Characters and Unipotent Blocks: 13. Levi subgroups and polynomial orders; 14. Unipotent characters as a basic set; 15. Jordan decomposition of characters; 16. On conjugacy classes in type D; 17. Standard isomorphisms for unipotent blocks; Part IV. Decomposition Numbers and q-Schur Algebras: 18. Some integral Hecke algebras; 19. Decomposition numbers and q-Schur algebras, general linear groups; 20. Decomposition numbers and q-Schur algebras, linear primes; Part V. Unipotent Blocks and Twisted Induction: 21. Local methods. Twisted induction for blocks; 22. Unipotent blocks and generalized Harish Chandra theory; 23. Local structure and ring structure of unipotent blocks; Appendix 1: Derived categories and derived functors; Appendix 2: Varieties and schemes; Appendix 3: Etale cohomology; References; Index.