Differential Geometry, Group Representations, and Quantization (Lecture Notes in Physics, Vol 379)
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Author: J.D. Hennig

Differential geometry and analytic group theory are among the most powerful tools in mathematical physics. This volume presents review articles on a wide variety of applications of these techniques in classical continuum physics, gauge theories, quantization procedures, and the foundations of quantum theory. The articles, written by leading scientists, address both researchers and grad uate students in mathematics, physics, and philosophy of science.


Lie Methods in Optics II: Proceedings of the Second Workshop Help at Cocoyoc, Mexico July 1922, 1988 (Lecture Notes in Physics 352)
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Nonlinearities in Action: Oscillations Chaos Order Fractals
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Author: A. V. GaponovGrekhov

In the dynamics of mankind one can trace out a path of contemplation about the "world", leading from early speculations to today's natural sciences. The endeavour to understand how nature works has led to the construction, still in progress, of an abstract building of great com plexity. To the uninitiated it may look more like a scurrilous sculpture resting on many legs, among them such peculiar ones as probability, relativity, quantum mechanics .... At times problems with the stabil ity of the building or sculpture arise: known facts that won't fit and can no longer be ignored start to undermine the foundations. Then new footings are thought of, constructed and finally cast. In fact, the undermining and casting is often done in one step. This process has already been repeated many times and will un doubtedly repeat itself again and again. At present, one recognizable footing under construction goes by the name of "chaos theory". Physi cists seem to like the word chaos. When they came to recognize that the air is not just empty space but an obviously indescribable dance of myriads of molecules they called that "chaos". What else would fit? In the course of time the name was simplified to "gas". Thus the word chaos became free to serve for the next upsetting experience. That arose in the context of nonlinear dynamical systems, where peculiar motions were detected, ones seemingly beyond human comprehension.


New Methods and Results in NonLinear Field Equations: Proc of a Conference Held at the University of Bielefeld, Fed. Rep. of Germany, 710 July 198 (Lecture Notes in Physics)
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Author: Philippe Blanchard



Analysis and Continuum Mechanics: A Collection of Papers Dedicated to J. Serrin on His Sixtieth Birthday
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Author: S. S. Antman

The 39 papers in this collection are devoted mostly to the exact mathematical analysis of problems in continuum mechanics, but also to problems of a purely mathematical nature mainly connected to partial differential equations from continuum physics. All the papers are dedicated to J. Serrin and were originally published in the "Archive of Rational Mechanics and Analysis".


Inverse Schrodinger Scattering in Three Dimensions (Texts & Monographs in Physics)
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Author: Roger G. Newton

Most of the laws of physics are expressed in the form of differential equations; that is our legacy from Isaac Newton. The customary separation of the laws of nature from contingent boundary or initial conditions, which has become part of our physical intuition, is both based on and expressed in the properties of solutions of differential equations. Within these equations we make a further distinction: that between what in mechanics are called the equations of motion on the one hand and the specific forces and shapes on the other. The latter enter as given functions into the former. In most observations and experiments the "equations of motion," i. e. , the structure of the differential equations, are taken for granted and it is the form and the details of the forces that are under investigation. The method by which we learn what the shapes of objects and the forces between them are when they are too small, too large, too remote, or too inaccessi ble for direct experimentation, is to observe their detectable effects. The question then is how to infer these properties from observational data. For the theoreti cal physicist, the calculation of observable consequences from given differential equations with known or assumed forces and shapes or boundary conditions is the standard task of solving a "direct problem. " Comparison of the results with experiments confronts the theoretical predictions with nature.


Group Theoretical Methods in Physics: Proceedings of the XVI International Colloquium (INTERNATIONAL COLLOQUIUM ON GROUP THEORETICAL METHODS IN ... THEORETICAL METHODS IN PHYSICS: PROCEEDINGS)
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Author: H. D. Doebner



Spinorial Chessboard (Trieste Notes in Physics)
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Author: P. Budinich

Spinor theory is an important tool in mathematical physics in particular in the context of conformal field theory and string theory. These lecture notes present a new way to introduce spinors by exploiting their intimate relationship to Clifford algebras. The presentation is detailed and mathematically rigorous. Not only students but also researchers will welcome this book for the clarity of its style and for the straightforward way it applies mathematical concepts to physical theory.


Theoretical Physics on the Personal Computer/Book and Disk (English and German Edition)
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Author: Erich W. Schmid

Theoretical Physics on the Personal Computer is a very successful, novel, easytocomprehend, and wellstructured text, ideal as an introduction to problemsolving with computers for advanced undergraduate students in physics and applied mathematics. The required Fortran 77 software for this book is included on a floppy disk. It has been designed for the IBM PC/XT, PC/AT, and PS/2, and for compatible computers such as the Siemens PCD2, etc., but it can also be run on mainframes. The second edition has not only been corrected and updated; with the new software the user can work with Microsoft Fortran (with or without a mathematical coprocessor) or the IBM Profort compiler (with coprocessor).


The Vector Coherent State Method and Its Application to Problems of Higher Symmetries (Lecture Notes in Physics)
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Author: K. T. Hecht

These lectures review the recently developed vector coherent state method. The book is an excellent introduction to the field because of the many examples treated in detail, in particular those from nuclear and particle physics. These calculations will be welcomed by researchers and graduate students. The author reviews the concepts of coherent states of the Heisenberg algebra and shows then that the vector coherent state method maps the higher symmetry algebra into an ndimensional harmonic oscillator algebra coupled with a simple intrinsic symmetry algebra. The formulation involves some vector (or analogous higher symmetry) coupling of the intrinsic algebra with the ndimensional oscillator algebra, leading to matrix representations and Wigner coefficients of the higher symmetry algebra expressed in terms of simple calculable functions and recoupling coefficients for the simpler intrinsic algebra.

