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The Wigner Symposium series is focussed on fundamental problems and new developments in physics and their experimental, theoretical and mathematical aspects. Particular emphasis is given to those topics which have developed from the work of Eugene P Wigner. The 2nd Wigner symposium is centered around notions of symmetry and geometry, the foundations of quantum mechanics, quantum optics and particle physics. Other fields like dynamical systems, neural networks and physics of information are also represented.This volume brings together 19 plenary lectures which survey latest developments and more than 130 contributed research reports.
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In this monograph, we shall present a new mathematical formulation of quantum theory, clarify a number of discrepancies within the prior formulation of quantum theory, give new applications to experiments in physics, and extend the realm of application of quantum theory well beyond physics. Here, we motivate this new formulation and sketch how it developed. Since the publication of Dirac's famous book on quantum mechanics [Dirac, 1930] and von Neumann's classic text on the mathematical foundations of quantum mechanics two years later [von Neumann, 1932], there have appeared a number of lines of development, the intent of each being to enrich quantum theory by extra polating or even modifying...
Philosophy of physics title by highly regarded author, fully revised for this paperback edition.
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 gives an overview of the recent representative developments in relativistic and non-relativistic quantum theory, which are related to the application of various mathematical notions of various symmetries. These notions are centered upon groups, algebras and their generalizations, and are applied in interaction with topology, differential geometry, functional analysis and related fields. The emphasis is on results in the following areas: foundation of quantum physics, quantization methods, nonlinear quantum mechanics, algebraic quantum field theory, gauge and string theories, discrete spaces, quantum groups and generalized symmetries.