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The present monograph provides a systematic and basicaIly self-eontained introduetion to a mathematieal framework eapable of ineOIporating those fundamental physical premises of general relativity and quantum meehanics which are not mutually ineonsistent, and which ean be therefore retained in the unifieation of these two fundamental areas of twentieth eentury physics. Thus, its underlying thesis is that the equivalenee principle of classical general relativity remains true at the quantum level, where it has to be reeonciled, however, with the uneertainty principle. As will be discussed in the first as weIl as in the last chapter, eonventional methods based on classical geometries and on single Hilbert space frame works for quantum meehanics have failed to aehieve such a reconciliation. On the other hand, foundational arguments suggest that new types of geometries should be introdueed. The geometries proposed and studied in this monograph are referred to as quantum geometries, sinee basic quantum principles are ineorporated into their strueture from the outset. The mathematical tools used in constructing these quantum geometries are drawn from functional analysis and fibre bundle theory, and in particular from Hilbert space the ory, group representation theory, and modern formulations of differential geometry. The developed physical eoncepts have their roots in nonrelativistic and relativistic quantum me chanics in Hilbert spaee, in classical general relativity and in quantum field theory for mas sive and gauge fields.
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Contenuti
Preface. 1. Principles and Physical Interpretation of Quantum Geometries. 2. The Fibre Framework for Classical General Relativity. 3. Stochastic Quantum Mechanics on Phase Space. 4. Nonrelativistic Newton-Carton Quantum Geometries. 5. Relativistic Klein-Gordon Quantum Geometries. 6. Relativistic Dirac Quantum Geometries. 7. Relativistic Quantum Geometries for Spin-O Massive Fields. 8. Relativistic Quantum Geometries for Spin-1/2 Massive Fields. 9. Quantum Geometries for Electromagnetic Fields. 10. Classical and Quantum Geometries for Yang-Mills Fields. 11. Geometro-Stochastic Quantum Gravity. 12. Historical and Epistemological Perpectives on Developments in Relativity and Quantum Theory. References. Index.
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Quantum Geometry : A Framework for Quantum General Relativity
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Quantum Geometry: A Framework for Quantum General Relativity (Fundamental Theories of Physics, 48)
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Quantum Geometry (Hardcover)
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Kluwer Academic Publishers, Dordrecht, 1992
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Hardcover. Condizione: new. Hardcover. This monograph presents a review and analysis of the main mathematical, physical and epistemological difficulties encountered at the foundational level by all the conventional formulations of relativistic quantum theories, ranging from relativistic quantum mechanics and quantum field theory in Minkowski space, to the various canonical and covariant approaches to quantum gravity. It is, however, primarily devoted to the systematic presentation of a quantum geometry framework meant to deal effectively with these difficulties by reconsidering the foundations of these subjects, analyzing their epistemic nature, and then developing mathematical tools which are specifically designed for the elimination of all the basic inconsistencies. The deficiencies of the conventional approaches are not usually discussed in the mainstream literature on these subjects, even though many of them were uncovered, and the need for their elimination was emphasized, by many founders of quantum theory, such as Born, Dirac, and Heisenberg.Hence, a historical survey is included, and additional extensive notes containing quotations from original sources are incorporated at the end of each chapter, so that the reader will be brought up-to-date with recent developments in quantum field theory in curved spacetime, quantum gravity and quantum cosmology. The survey further provides a backdrop against which the new foundational and mathematical ideas of the present approach to these subjects can be brought out in sharper relief. These ideas reflect the legacy of the founders of relativity and quantum theory, as they are attempting to find a common ground in the apparently irreconcilable points of view of Bohr and Einstein. In developing them, as much attention is devoted to incorporating them into a mathematically sound framework for relativistic quantum theory, advocated by Dirac, as to securing their epistemological soundness, reflected by a clear enunciation of all the underlying physcial principles, whose need was stressed by Heisenberg.This work is aimed at theoretical and mathematical physicists, mathematicians interested in differential geometry, fibre bundles, and global analysis, philosophers and historians of sciences interested in general relativity and quantum theory. Despite the advanced level of many of the areas of mathematics and theoretical physics treated, every effort has been made to produce a text which is also accessible to graduate students in physics and mathematics. Presents a review and analysis of the main mathematical, physical and epistomological difficulties encountered at the foundational level by various conventional formulations of relativistic quantum theories. This title includes a survey which offers developments in quantum field theory in curved spacetime, quantum gravity and quantum cosmology. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Codice articolo 9780792316404
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Quantum Geometry
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Gebunden. Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Preface. 1. Principles and Physical Interpretation of Quantum Geometries. 2. The Fibre Framework for Classical General Relativity. 3. Stochastic Quantum Mechanics on Phase Space. 4. Nonrelativistic Newton-Carton Quantum Geometries. 5. Relativistic Klein. Codice articolo 5966482
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Quantum Geometry: A Framework for Quantum General Relativity (Fundamental Theories of Physics, 48)
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Quantum Geometry
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Springer Netherlands, Springer Netherlands Feb 1992, 1992
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Buch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -The present monograph provides a systematic and basicaIly self-eontained introduetion to a mathematieal framework eapable of ineOIporating those fundamental physical premises of general relativity and quantum meehanics which are not mutually ineonsistent, and which ean be therefore retained in the unifieation of these two fundamental areas of twentieth eentury physics. Thus, its underlying thesis is that the equivalenee principle of classical general relativity remains true at the quantum level, where it has to be reeonciled, however, with the uneertainty principle. As will be discussed in the first as weIl as in the last chapter, eonventional methods based on classical geometries and on single Hilbert space frame works for quantum meehanics have failed to aehieve such a reconciliation. On the other hand, foundational arguments suggest that new types of geometries should be introdueed. The geometries proposed and studied in this monograph are referred to as quantum geometries, sinee basic quantum principles are ineorporated into their strueture from the outset. The mathematical tools used in constructing these quantum geometries are drawn from functional analysis and fibre bundle theory, and in particular from Hilbert space the ory, group representation theory, and modern formulations of differential geometry. The developed physical eoncepts have their roots in nonrelativistic and relativistic quantum me chanics in Hilbert spaee, in classical general relativity and in quantum field theory for mas sive and gauge fields.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 548 pp. Englisch. Codice articolo 9780792316404
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Quantum Geometry : A Framework for Quantum General Relativity
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Springer Netherlands, Springer Netherlands, 1992
ISBN 10: 0792316401
ISBN 13: 9780792316404
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Buch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - The present monograph provides a systematic and basicaIly self-eontained introduetion to a mathematieal framework eapable of ineOIporating those fundamental physical premises of general relativity and quantum meehanics which are not mutually ineonsistent, and which ean be therefore retained in the unifieation of these two fundamental areas of twentieth eentury physics. Thus, its underlying thesis is that the equivalenee principle of classical general relativity remains true at the quantum level, where it has to be reeonciled, however, with the uneertainty principle. As will be discussed in the first as weIl as in the last chapter, eonventional methods based on classical geometries and on single Hilbert space frame works for quantum meehanics have failed to aehieve such a reconciliation. On the other hand, foundational arguments suggest that new types of geometries should be introdueed. The geometries proposed and studied in this monograph are referred to as quantum geometries, sinee basic quantum principles are ineorporated into their strueture from the outset. The mathematical tools used in constructing these quantum geometries are drawn from functional analysis and fibre bundle theory, and in particular from Hilbert space the ory, group representation theory, and modern formulations of differential geometry. The developed physical eoncepts have their roots in nonrelativistic and relativistic quantum me chanics in Hilbert spaee, in classical general relativity and in quantum field theory for mas sive and gauge fields. Codice articolo 9780792316404
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Quantum Geometry
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