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This book presents the up-to-date status of quantum theory and the outlook for its development in the 21st century. The covered topics include basic problems of quantum physics, with emphasis on the foundations of quantum theory, quantum computing and control, quantum optics, coherent states and Wigner functions, as well as on methods of quantum physics based on Lie groups and algebras, quantum groups and noncommutative geometry.
The Standard Model of elementary particles, although very successful, contains various elements that are put in by hand. Understanding their origin requires going beyond the model and searching for “new physics”. The present book elaborates on one particular proposal concerning such physics. While the original conception is 50 years old, it has not lost its appeal over time. Its basic idea is that space — an arena of events treated in the Standard Model as a classical background — is a concept which emerges from a strictly discrete quantum layer in the limit of large quantum numbers. This book discusses an extension of this view by replacing space with phase space. It combines the results of the author's research papers and places them in much broader philosophical and phenomenological contexts, thus providing further arguments in favor of the proposed alternative. The book should be of interest to the philosophically-minded readers who are willing to contemplate unorthodox ideas on the very nature of the world.
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.
The Olympia conference Frontiers of Fundamental Physics was a gathering of about hundred scientists who carryon their research in conceptually important areas of physical science (they do "fundamental physics"). Most of them were physicists, but also historians and philosophers of science were well represented. An important fraction of the participants could be considered "heretical" because they disagreed with the validity of one or several fundamental assumptions of modern physics. Common to all participants was an excellent scientific level coupled with a remarkable intellectual honesty: we are proud to present to the readers this certainly unique book. Alternative ways of considering fun...
The so-far unanswered question of whether the movements of distance-separated objects are correlated in the way quantum physics requires or whether, according to Einstein, they can influence one another only by mechanical agencies travelling between them at speeds limited to that of light. It is to that still unanswered question that this present compilation of papers is addressed. The editorial approach is unusual in that in order to break the current conceptual deadlock and to encourage true innovation they have solicited inputs which are multidisciplinary. This open-ended venture is therefore perhaps more in line with what was once called Natural Philosophy than with what is currently kno...
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