Quantum Versus Classical Mechanics and Integrability Problems: Towards a Unification of Approaches and Tools, Blaszak Maciej
Автор: Maciej B?aszak Название: Quantum versus Classical Mechanics and Integrability Problems ISBN: 3030183785 ISBN-13(EAN): 9783030183783 Издательство: Springer Рейтинг: Цена: 102480.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
This accessible monograph introduces physicists to the general relation between classical and quantum mechanics based on the mathematical idea of deformation quantization and describes an original approach to the theory of quantum integrable systems developed by the author.
The first goal of the book is to develop of a common, coordinate free formulation of classical and quantum Hamiltonian mechanics, framed in common mathematical language.
In particular, a coordinate free model of quantum Hamiltonian systems in Riemannian spaces is formulated, based on the mathematical idea of deformation quantization, as a complete physical theory with an appropriate mathematical accuracy.
The second goal is to develop of a theory which allows for a deeper understanding of classical and quantum integrability. For this reason the modern separability theory on both classical and quantum level is presented. In particular, the book presents a modern geometric separability theory, based on bi-Poissonian and bi-presymplectic representations of finite dimensional Liouville integrable systems and their admissible separable quantizations.
The book contains also a generalized theory of classical St?ckel transforms and the discussion of the concept of quantum trajectories.
In order to make the text consistent and self-contained, the book starts with a compact overview of mathematical tools necessary for understanding the remaining part of the book. However, because the book is dedicated mainly to physicists, despite its mathematical nature, it refrains from highlighting definitions, theorems or lemmas.
Nevertheless, all statements presented are either proved or the reader is referred to the literature where the proof is available.
Автор: Zoran Majkic Название: Completion and Unification of Quantum Mechanics with Einsteins GR Ideas PART III: Advances, Revisions and Conclusions ISBN: 1536172006 ISBN-13(EAN): 9781536172003 Издательство: Nova Science Рейтинг: Цена: 215410.00 T Наличие на складе: Невозможна поставка. Описание: Quantum mechanics, based on the SchrA¶dinger equation (and its relativistic Diracs extension) is a statistical theory, here denominated as Statistical Quantum Mechanics (SQM), to differentiate it from the new part of the quantum theory, provided in PART I and II, denominated Individual-particles Quantum Mechanics (IQM). Both of them are necessary components of the quantum theory, as are the Classical Mechanics for Individual objects (ICM), based on the Newton equations, Hamiltonian-Jacobi equations or the Euler-Lagrange equation of motion of individual objects, and the Statistical Classical Mechanics (SCM) based on the Liouville equations. The SQM tells us the various possible outcomes of experiments and the corresponding probabilities if we would do a large number of identical experiments on individual quantum systems. The SQM systems are not all identical but this is the same type of fluctuation that occurs in classical statistical descriptions in SCM. At first sight the situation may not appear very different therefore from the description provided by classical statistical mechanics. In that case however, we have an underlying description (ICM) that provides a complete (i.e. non-statistical) description of the world, which in general is far too complex, however, to be of use. The last PART III of this trilogy is dedicated to the completion of the whole theoretical mechanics, both classical and quantum inside a 9-D time-space manifold of the Universe. Only in this final third volume, this IQM theory, dedicated in the first two volumes only to the elementary particles, is extended also to the non-elementary particles (like hadrons, nucleus, atoms, molecules, and all every-day objects in our common life, up to the biggest non-elementary particles, like the planets, stars, etc.) in our unique Universe. So, each object in our Universe, from the smallest (elementary) to the biggest, can be mathematically expressed by the same mathematical 9-D complex field expression, in a unifying way at which the physical determinism holds for the individual objects at all micro-macro scales in our Universe.
Автор: Zoran Majkic Название: Completion & Unification of Quantum Mechanics with Einsteins GR Ideas: Part I -- Completion of QM ISBN: 1536119466 ISBN-13(EAN): 9781536119466 Издательство: Nova Science Рейтинг: Цена: 257650.00 T Наличие на складе: Невозможна поставка. Описание: This unique manuscript presents a novel approach to QM by modelling an elementary particle via 3D matter/energy density, which propagates in the open time-space continuum as a rest mass energy density wave packet. This simple idea is based on the fact that any macroscopic object of mass M that occupies a finite 3D volume V can be represented by an energy-density contained in V, so that the integration of this energy-density over V provides the total energy E = Mc^2 . This new theory is fully integrated with the theory of relativity, and completes the quantum theory of Einstein by overcoming the Copenhagen interpretation. The newly introduced partial differential equations describe the relativistic phenomena and, generally, the dependence of a particles geometrical form (its internal matter distribution) on its velocity and acceleration. A number of well-known physical principles are obtained as derived results of this theory, and are consolidated by a number of detailed examples. Part I, which is dedicated to the completion of QM, is composed of five Chapters. In the first two chapters, the nucleus is analysed in terms of the material discussed. Chapter Three is dedicated to the development of the Lagrangian density for the complex wave packets of the rest mass energy density of an elementary particle, and to the new quantum field theory. The authors obtained the set of new non-Hamiltonian TSPF quantum operators, parameterised by the vector velocity field of energy density with corresponding Hilbert spaces for accelerated particles, and these were valid in any (infinitesimal) local Minkowski time-space. The main results are the new differential equations obtained as conservation laws for Noether currents and Euler-Lagrange equations, which express the exact form of the complex terms used in the differential equations in Chapters One and Two, and introduce the most useful concept of the velocity for any infinitesimal amount of the energy density flux of a particle (the hidden variables). In Chapter Four, a gauge theory and a new explanation of the mass gap conjecture in Yang-Mils theory and of the Higgs mechanism without necessity of the new Higgs field and its bosons, along with a new explanation of double-slit experiments are presented. Thus, the authors obtained a conservative extension of current probabilistic/statistic QM valid for an ensemble of particles, each individual particle, and which is deterministic and compatible by classical mechanics.
Автор: Hsu Jong-Ping Et Al Название: Space-Time Symmetry And Quantum Yang-Mills Gravity: How Space-Time Translational Gauge Symmetry Enables The Unification Of Gravity With Other Forces ISBN: 9814436186 ISBN-13(EAN): 9789814436182 Издательство: World Scientific Publishing Рейтинг: Цена: 95040.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Yang-Mills gravity is a new theory, consistent with experiments, that brings gravity back to the arena of gauge field theory and quantum mechanics in flat space-time. It provides solutions to long-standing difficulties in physics, such as the incompatibility between Einstein's principle of general coordinate invariance and modern schemes for a quantum mechanical description of nature, and Noether's 'Theorem II' which showed that the principle of general coordinate invariance in general relativity leads to the failure of the law of conservation of energy. Yang-Mills gravity in flat space-time appears to be more physically coherent than conventional gravity in curved space-time. The problems of quantization of the gravitational field, the operational meaning of space-time coordinates and momenta, and the conservation of energy-momentum are all resolved in Yang-Mills gravity.The aim of this book is to provide a treatment of quantum Yang-Mills gravity, with an emphasis on the ideas and evidence that the gravitational field is the manifestation of space-time translational symmetry in flat space-time, and that there exists a fundamental space-time symmetry framework that can encompass all of physics, including gravity, for all inertial and non-inertial frames of reference.
Автор: Behram N. Kursunogammalu; Stephan L. Mintz; Arnold Название: Quantum Gravity, Generalized Theory of Gravitation, and Superstring Theory-Based Unification ISBN: 1441933484 ISBN-13(EAN): 9781441933485 Издательство: Springer Рейтинг: Цена: 139710.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Held December 16-919, 1999, this proceedings is derived from the Global Foundation Inc.`s Orbis Scientiae 1999. Topics include: cosmological parameters, unifying elementary particle physics, cosmology, superstrings, and black holes.
Автор: A. Ceresole; C. Kounnas; D. L?st; S. Theisen Название: Quantum Aspects of Gauge Theories, Supersymmetry and Unification ISBN: 3662142538 ISBN-13(EAN): 9783662142530 Издательство: Springer Рейтинг: Цена: 104480.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The articles in this book are written versions of talks presented at a conference organized by the TMR network in Corfu. The main theme of the conference was the interconnection between string theory and gauge theory. These very recent developments draw from many aspects of string theory, supergravity and supersymmetric gauge field theory.
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