The Complex Wkb Method for Nonlinear Equations I: Linear Theory (Progress in Mathematical Physics)
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Author: V. P. Maslov

When first published (in Russian), this book proved to become the fountainhead of a major stream of important papers in mathematics, physics and even chemistry. Indeed, it formed the basis of new methodology and opened new directions for research. The present English edition includes new examples of applications to physics, hitherto unpublished or available only in Russian. It uses topological methods to analyze isotropic invariant manifolds in order to obtain symptotic series of eigenvalues and eigenvectors for the multidimensional SchrĂ¶dinger equation also taking into account the socalled tunnel effects.


Integrable Structures of Exactly Solvable Two Dimensional Models of Quantum Field Theory
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Integrable quantum field theories and integrable lattice models have been studied for several decades, but during the last few years new ideas have emerged that have considerably changed the topic. The first group of papers published here is concerned with integrable structures of quantum lattice models related to quantum group symmetries. The second group deals with the description of integrable structures in twodimensional quantum field theories, especially boundary problems, thermodynamic Bethe ansatz and form factor problems. Finally, a major group of papers is concerned with the purely mathematical framework that underlies the physicallymotivated research on quantum integrable models, including elliptic deformations of groups, representation theory of noncompact quantum groups, and quantization of moduli spaces.
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The Theory of Finslerian Laplacians and Applications (Mathematics and Its Applications)
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Brand: Brand: Springer

Finslerian Laplacians have arisen from the demands of modelling the modern world. However, the roots of the Laplacian concept can be traced back to the sixteenth century. Its phylogeny and history are presented in the Prologue of this volume. The text proper begins with a brief introduction to stochastically derived Finslerian Laplacians, facilitated by applications in ecology, epidemiology and evolutionary biology. The mathematical ideas are then fully presented in section II, with generalizations to Lagrange geometry following in section III. With section IV, the focus abruptly shifts to the local meanvalue approach to Finslerian Laplacians and a Hodgede Rham theory is developed for the representation on real cohomology classes by harmonic forms on the base manifold. Similar results are proved in sections II and IV, each from different perspectives. Modern topics treated include nonlinear Laplacians, Bochner and Lichnerowicz vanishing theorems, WeitzenbĂ¶ck formulas, and Finslerian spinors and Dirac operators. The tools developed in this book will find uses in several areas of physics and engineering, but especially in the mechanics of inhomogeneous media, e.g. Cofferat continua. Audience: This text will be of use to workers in stochastic processes, differential geometry, nonlinear analysis, epidemiology, ecology and evolution, as well as physics of the solid state and continua.
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The Mathematical Analysis of Physical Systems
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Author: Ronald Mickens

Contents: 11. The Unreasonable Effectiveness of Mathematics in the Natural Sciences / Eugene P. Wigner; 12. The Unreasonable Effectiveness of Mathematics / R.W. Hamming; 2. Gauge Invariance in Nature: A Simple View / Sylvester J. Gates, Jr.; 3. The Radon Transform / Stanley R. Deans; 4. The Geometry of Quantum Flow / James V. Lindesay and Harry L. Morrison; 5. Classical Chaos, the Geometry of Phase Space, and Semiclassical Quantization / William P. Reinhardt; 6. The Adiabatic Method in the Theory of ManyBody Systems / Vladimir Z. Kresin and William A. Lester, Jr.; 7. Catastrophe Theory: What It Is, Why It Exists, How It Works / Robert Gilmore


A Course in Mathematical Physics: Volume 2: Classical Field Theory
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Author: Walter Thirring

Combining the corrected editions of both volumes on classical physics of Thirring's course in mathematical physics, this treatment of classical dynamical systems employs analysis on manifolds to provide the mathematical setting for discussions of Hamiltonian systems. Problems discussed in detail include nonrelativistic motion of particles and systems, relativistic motion in electromagnetic and gravitational fields, and the structure of black holes. The treatment of classical fields uses differential geometry to examine both Maxwell's and Einstein's equations with new material added on guage theory.


Geometric and Quantum Aspects of Integrable Systems: Proceedings of the Eighth Scheveningen Conference Scheveningen, the Netherlands, August 1621, 1 (Lecture Notes in Physics, 424)
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Author: Scheveningen Conference 1992

This is a collection of outstanding review papers on integrable systems. It gives the algebraic geometric aspects of the subject, describes integrability techniques e.g. for the modified KdV equation, integrability of Hamiltonian systems, hierarchies of equations, probability distribution of eigenvalues, and modern aspects of quantum groups. It addresses researchers in mathematics and mathematical physics.


Theoretical Physics: A Classical Approach
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Author: Josef Honerkamp

Theoretical Physics is a thorough introduction to classical theoretical physics. While concise in its use of terminology, the book is intended to provide the means to understand the fundamentals of this field. Worked examples throughout the text and 39 problems help the student to become familiar with the physics presented here. With a view to achieving completeness, statistical mechanics, thermodynamics, and fluid dynamics are also discussed. After careful study of the book the student will be familiar with a wide variety of fields from advanced theoretical physics or applied physics.


Mathematical Physics X: Proceedings of the Xth Congress on Mathematical Physics : Held at Leipzig, Germany, 30 July9 August, 1991
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Advances in the FreeLagrange Method: Including Contributions on Adaptive Gridding and the Smooth Particle Hydrodynamics Method : Proceedings of the (Lecture Notes in Physics, 395)
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Author: Wyo.) Next FreeLagrange Conference (1990 Moran
Brand: Brand: SpringerVerlag

The contributions in this volume focus on the use of general connectivity (unstructured) adaptive meshes for Lagrangian calculations but contain a substantial amount of material on Euler and arbitrary LagrangeEuler techniques as well. Contributions on the smooth particle hydrodynamics method and on deterministic vortex methods broaden the scope of the material and allow comparisons of different, though allied, techniques to be made. The format of the conference was designedto optimize the interaction among the attendees. An edited version of roundtable discussions is included in these proceedings.
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Group Theoretical Methods in Physics: Proceedings of the XVII International Colloquium Held at Moscow, Ussr, 49 June 1990 (INTERNATIONAL COLLOQUIUM ... THEORETICAL METHODS IN PHYSICS: PROCEEDINGS)
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Author: V. V. Dodonov

This volume contains review talks and a small selection of the research papers presented at the world's most distinguished conference on group theoretical methods in physics. The papers are devoted to such topics as spectrum generating groups, quantum groups, coherent states, and geometric aspects of group representations. The methods apply to nuclear physics, quantum mechanics, ordinary and supersymmetric linear and non linear differential equations, geometry, and noncommutative geometry. The book addresses theoretical physicists, especially those in research.

