Dobrev Vladimir K Dobrev – författare

This volume is targeted at theoretical physicists, mathematical physicists and mathematicians working on mathematical models for physical systems based on symmetry methods and in the field of Lie theory understood in the widest sense. It includes contributions on Lie theory, with two papers by the famous mathematician Kac (one paper with Bakalov), further papers by Aoki, Moens. Some other important contributions are in: field theory - Todorov, Grosse, Kreimer, Sokatchev, Gomez; string theory — Minwalla, Staudacher, Kostov; integrable systems - Belavin, Helminck, Ragoucy; quantum-mechanical and probabilistic systems — Goldin, Van der Jeugt, Leandre; quantum groups and related objects — Jakobsen, Arnaudon, Andruskiewitsch; and others.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings)• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences

This volume gives a representative survey of recent developments in relativistic and non-relativistic quantum theory, which are related to the application of symmetries in their most general sense. The corresponding mathematical notions are centered upon groups, algebras and their generalizations, and are applied in interaction with topology, differential geometry, functional analysis and related fields. Special emphasis is on results in the following areas: quantization methods, nonlinear evolution equations, foundation of quantum physics, algebraic quantum field theory, gauge and string theories, quantum information, quantum groups, discrete symmetries.

There is an apparent trend towards geometrization of physical theories. During the last 20 years, the most successful mathematical models for the description and understanding of physical systems have been based on the Lie theory in its widest sense and various generalizations, for example, deformations of it.This proceedings volume reflects part of the development. On the mathematical side, they report on representations of Lie algebras, quantization procedures, non-commutative geometry, quantum groups, etc. Furthermore, possible physical applications of these techniques are discussed (e.g. quantization of classical systems, derivations of evolution equations, discrete and deformed physical systems).This volume complements the book Generalized Symmetries in Physics, published by World Scientific in 1994.

In recent years nonlinear and irreversible quantum mechanics is becoming increasingly important because of the availability of precision experiments. There are new and successful attempts to understand quantum irreversibility. The development of generalized symmetries has to led to new families of evolution equations for pure and mixed states. On the one hand, this timely symposium covers nonlinear and irreversible quantum mechanics, the theory of quantization methods, causality and various problems important in this context. On the other hand, it reports the development of quantum group symmetries, and of methods to construct deformed quantum mechanical evolution equations like the q-deformed Schrödinger equations.

This volume contains material submitted to a symposium on mathematical physics in July 1993 at the Technical University of Clausthal. It focuses on mathematical and physical notions of symmetries, especially on generalized and quantum symmetries (quantum groups and algebras) with applications to integrable systems, quasi-exact solvability, quantization methods and nonlinear problems. The workshop is a continuation of the series of meetings and workshops on mathematical physics in Clausthal which brings together mathematicians, theoretical and mathematical physicists working in the different parts of generalized symmetries. Recent developments in the mathematical structure and physical applications of generalized symmetries are discussed.