Geometrodynamics of Gauge Fields
Author: Eckehard W. Mielke
Publisher: Walter de Gruyter GmbH & Co KG
Published: 1987-12-31
Total Pages: 244
ISBN-13: 3112766075
DOWNLOAD EBOOKNo detailed description available for "Geometrodynamics of Gauge Fields".
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Geometrodynamics of Gauge Fields
Author: Eckehard W. Mielke
Publisher: Springer
Published: 2017-01-22
Total Pages: 377
ISBN-13: 3319297341
DOWNLOAD EBOOKThis monograph aims to provide a unified, geometrical foundation of gauge theories of elementary particle physics. The underlying geometrical structure is unfolded in a coordinate-free manner via the modern mathematical notions of fibre bundles and exterior forms. Topics such as the dynamics of Yang-Mills theories, instanton solutions and topological invariants are included. By transferring these concepts to local space-time symmetries, generalizations of Einstein's theory of gravity arise in a Riemann-Cartan space with curvature and torsion. It provides the framework in which the (broken) Poincaré gauge theory, the Rainich geometrization of the Einstein-Maxwell system, and higher-dimensional, non-abelian Kaluza-Klein theories are developed. Since the discovery of the Higgs boson, concepts of spontaneous symmetry breaking in gravity have come again into focus, and, in this revised edition, these will be exposed in geometric terms. Quantizing gravity remains an open issue: formulating it as a de Sitter type gauge theory in the spirit of Yang-Mills, some new progress in its topological form is presented. After symmetry breaking, Einstein’s standard general relativity with cosmological constant emerges as a classical background. The geometrical structure of BRST quantization with non-propagating topological ghosts is developed in some detail.
Topological Geometrodynamics
Author: Matti Pitkanen
Publisher: Luniver Press
Published: 2006
Total Pages: 822
ISBN-13: 0955117089
DOWNLOAD EBOOKTopological GeometroDynamics is a modification of general relativity inspired by the conceptual problems related to the definitions of inertial and gravitational energy in general relativity. Topological geometrodynamics can be also seen as a generalization of super string models. Physical space-times are seen as four-dimensional surfaces in certain eight-dimensional space. The choice of this space is fixed by symmetries of the standard model so that geometrization of known classical fields and elementary particle quantum numbers results. The notion of many-sheeted space-time allows re-interpretation of the structures of perceived world in terms of macroscopic space-time topology. The generalization of the number concept based on fusion of real numbers and p-adic number fields implies a further generalization of the space-time concept allowing to identify space-time correlates of cognition and intentionality. Quantum measurement theory extended to a quantum theory of consciousness becomes an organic part of theory. A highly non-trivial prediction is the existence of a fractal hierarchy of copies of standard model physics with dark matter identified in terms of macroscopic quantum phases characterized by dynamical and quantized Planck constant. The book is a comprehensive overview and analysis of topological geometrodynamics as a mathematical and physical theory.
Gravity, Gauge Theories and Quantum Cosmology
Author: J.V. Narlikar
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 477
ISBN-13: 9400945086
DOWNLOAD EBOOKFor several decades since its inception, Einstein's general theory of relativity stood somewhat aloof from the rest of physics. Paradoxically, the attributes which normally boost a physical theory - namely, its perfection as a theoreti cal framework and the extraordinary intellectual achievement underlying i- prevented the general theory from being assimilated in the mainstream of physics. It was as if theoreticians hesitated to tamper with something that is manifestly so beautiful. Happily, two developments in the 1970s have narrowed the gap. In 1974 Stephen Hawking arrived at the remarkable result that black holes radiate after all. And in the second half of the decade, particle physicists discovered that the only scenario for applying their grand unified theories was offered by the very early phase in the history of the Big Bang universe. In both cases, it was necessary to discuss the ideas of quantum field theory in the background of curved spacetime that is basic to general relativity. This is, however, only half the total story. If gravity is to be brought into the general fold of theoretical physics we have to know how to quantize it. To date this has proved a formidable task although most physicists would agree that, as in the case of grand unified theories, quantum gravity will have applications to cosmology, in the very early stages of the Big Bang universe. In fact, the present picture of the Big Bang universe necessarily forces us to think of quantum cosmology.
Gauge Theories of Gravitation
Author: Friedrich W. Hehl
Publisher: World Scientific Publishing Company Incorporated
Published: 2013
Total Pages: 635
ISBN-13: 9781848167261
DOWNLOAD EBOOKForeword by T W B Kibble, FRSIn the last five decades, the gauge approach to gravity has represented a research area of increasing importance for our understanding of the physics of fundamental interactions. A full clarification of the gauge dynamics of gravity is expected to be the last missing link to the hidden structure of a consistent unification of all the fundamental interactions, based on the gauge principle. The aim of the present reprint volume, with commentaries by Milutin Blagojević and Friedrich W Hehl, is to introduce graduate and advanced undergraduate students of theoretical or mathematical physics, or any other interested researcher, to the field of classical gauge theories of gravity.This is not just an ordinary reprint volume; it is a guide to the literature on gauge theories of gravity. The reader is encouraged first to study the introductory commentaries and to become familiar with the basic content of the reprints and related ideas, then he/she can choose to read a specific reprint or reprints, and after that he/she should return again to the text and explore the additional literature, etc. The interaction is intended to be more complex than just starting with commentaries and ending with reprints.
Modern Differential Geometry in Gauge Theories
Author: Anastasios Mallios
Publisher: Springer Science & Business Media
Published: 2006-07-27
Total Pages: 303
ISBN-13: 0817644741
DOWNLOAD EBOOKThis is original, well-written work of interest Presents for the first time (physical) field theories written in sheaf-theoretic language Contains a wealth of minutely detailed, rigorous computations, ususally absent from standard physical treatments Author's mastery of the subject and the rigorous treatment of this text make it invaluable
Gauge Field Theory in Natural Geometric Language
Author: Daniel Canarutto
Publisher: Oxford University Press
Published: 2020-10-06
Total Pages: 330
ISBN-13: 0192606212
DOWNLOAD EBOOKGauge Field theory in Natural Geometric Language addresses the need to clarify basic mathematical concepts at the crossroad between gravitation and quantum physics. Selected mathematical and theoretical topics are exposed within a brief, integrated approach that exploits standard and non-standard notions, as well as recent advances, in a natural geometric language in which the role of structure groups can be regarded as secondary even in the treatment of the gauge fields themselves. In proposing an original bridge between physics and mathematics, this text will appeal not only to mathematicians who wish to understand some of the basic ideas involved in quantum particle physics, but also to physicists who are not satisfied with the usual mathematical presentations of their field.
Connections in Classical and Quantum Field Theory
Author: L. Mangiarotti
Publisher: World Scientific
Published: 2000
Total Pages: 518
ISBN-13: 9789812813749
DOWNLOAD EBOOKGeometrical notions and methods play an important role in both classical and quantum field theory, and a connection is a deep structure which apparently underlies the gauge-theoretical models. This collection of basic mathematical facts about various types of connections provides a detailed description of the relevant physical applications. It discusses the modern issues concerning the gauge theories of fundamental interactions. This text presents several levels of complexity, from the elementary to the advanced, and provides a considerable number of exercises. The authors have tried to give all the necessary mathematical background, thus making the book self-contained. This book should be useful to graduate students, physicists and mathematicians who are interested in the issue of deep interrelations between theoretical physics and geometry.
Stochastic Quantum Mechanics and Quantum Spacetime
Author: Margaret Prugovecki
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 319
ISBN-13: 9400944926
DOWNLOAD EBOOKThe principal intent of this monograph is to present in a systematic and self-con tained fashion the basic tenets, ideas and results of a framework for the consistent unification of relativity and quantum theory based on a quantum concept of spacetime, and incorporating the basic principles of the theory of stochastic spaces in combination with those of Born's reciprocity theory. In this context, by the physicial consistency of the present framework we mean that the advocated approach to relativistic quantum theory relies on a consistent probabilistic interpretation, which is proven to be a direct extrapolation of the conventional interpretation of nonrelativistic quantum mechanics. The central issue here is that we can derive conserved and relativistically convariant probability currents, which are shown to merge into their nonrelativistic counterparts in the nonrelativistic limit, and which at the same time explain the physical and mathe matical reasons behind the basic fact that no probability currents that consistently describe pointlike particle localizability exist in conventional relativistic quantum mechanics. Thus, it is not that we dispense with the concept oflocality, but rather the advanced central thesis is that the classical concept of locality based on point like localizability is inconsistent in the realm of relativistic quantum theory, and should be replaced by a concept of quantum locality based on stochastically formulated systems of covariance and related to the aforementioned currents.
Stochastic Quantum Mechanics and Quantum Spacetime
Author: Eduard Prugovečki
Publisher: Springer Science & Business Media
Published: 1984-01-31
Total Pages: 334
ISBN-13: 9789027716170
DOWNLOAD EBOOKThe principal intent of this monograph is to present in a systematic and self-con tained fashion the basic tenets, ideas and results of a framework for the consistent unification of relativity and quantum theory based on a quantum concept of spacetime, and incorporating the basic principles of the theory of stochastic spaces in combination with those of Born's reciprocity theory. In this context, by the physicial consistency of the present framework we mean that the advocated approach to relativistic quantum theory relies on a consistent probabilistic interpretation, which is proven to be a direct extrapolation of the conventional interpretation of nonrelativistic quantum mechanics. The central issue here is that we can derive conserved and relativistically convariant probability currents, which are shown to merge into their nonrelativistic counterparts in the nonrelativistic limit, and which at the same time explain the physical and mathe matical reasons behind the basic fact that no probability currents that consistently describe pointlike particle localizability exist in conventional relativistic quantum mechanics. Thus, it is not that we dispense with the concept oflocality, but rather the advanced central thesis is that the classical concept of locality based on point like localizability is inconsistent in the realm of relativistic quantum theory, and should be replaced by a concept of quantum locality based on stochastically formulated systems of covariance and related to the aforementioned currents.
