Geometrical Quantum Mechanics
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Geometric Formulation Of Classical And Quantum Mechanics
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Author : G. Giachetta
language : en
Publisher: World Scientific
Release Date : 2011
Geometric Formulation Of Classical And Quantum Mechanics written by G. Giachetta and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Science categories.
The geometric formulation of autonomous Hamiltonian mechanics in the terms of symplectic and Poisson manifolds is generally accepted. This book provides the geometric formulation of non-autonomous mechanics in a general setting of time-dependent coordinate and reference frame transformations.
Symplectic Geometry And Quantum Mechanics
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Author : Maurice A. de Gosson
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-08-06
Symplectic Geometry And Quantum Mechanics written by Maurice A. de Gosson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-06 with Mathematics categories.
This book offers a complete discussion of techniques and topics intervening in the mathematical treatment of quantum and semi-classical mechanics. It starts with a very readable introduction to symplectic geometry. Many topics are also of genuine interest for pure mathematicians working in geometry and topology.
Geometrical Quantum Mechanics
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Author : Robert Geroch
language : en
Publisher: Minkowski Institute Press
Release Date : 2013-03-23
Geometrical Quantum Mechanics written by Robert Geroch and has been published by Minkowski Institute Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-23 with Science categories.
Geroch's lecture notes on geometrical quantum mechanics are divided into three parts - Differential Geometry, Mechanics, and Quantum Mechanics. The necessary geometrical ideas are presented in the first part of the book and are applied to mechanics and quantum mechanics in the second and third part. What also makes this book a valuable contribution to the existing textbooks on quantum physics is Geroch's unique approach to teaching theoretical and mathematical physics - the physical concepts and the mathematics, which describes them, are masterfully intertwined in such a way that both reinforce each other to facilitate the understanding of even the most abstract and subtle issues.
Geometric Phases In Classical And Quantum Mechanics
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Author : Dariusz Chruscinski
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometric Phases In Classical And Quantum Mechanics written by Dariusz Chruscinski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Several well-established geometric and topological methods are used in this work in an application to a beautiful physical phenomenon known as the geometric phase. This book examines the geometric phase, bringing together different physical phenomena under a unified mathematical scheme. The material is presented so that graduate students and researchers in applied mathematics and physics with an understanding of classical and quantum mechanics can handle the text.
Geometric Quantization And Quantum Mechanics
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Author : Jedrzej Sniatycki
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometric Quantization And Quantum Mechanics written by Jedrzej Sniatycki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
This book contains a revised and expanded version of the lecture notes of two seminar series given during the academic year 1976/77 at the Department of Mathematics and Statistics of the University of Calgary, and in the summer of 1978 at the Institute of Theoretical Physics of the Technical University Clausthal. The aim of the seminars was to present geometric quantization from the point of view· of its applica tions to quantum mechanics, and to introduce the quantum dynamics of various physical systems as the result of the geometric quantization of the classical dynamics of these systems. The group representation aspects of geometric quantiza tion as well as proofs of the existence and the uniqueness of the introduced structures can be found in the expository papers of Blattner, Kostant, Sternberg and Wolf, and also in the references quoted in these papers. The books of Souriau (1970) and Simms and Woodhouse (1976) present the theory of geometric quantization and its relationship to quantum mech anics. The purpose of the present book is to complement the preceding ones by including new developments of the theory and emphasizing the computations leading to results in quantum mechanics.
Geometric And Algebraic Topological Methods In Quantum Mechanics
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Author : G. Giachetta
language : en
Publisher: World Scientific
Release Date : 2005
Geometric And Algebraic Topological Methods In Quantum Mechanics written by G. Giachetta and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Science categories.
In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry''s geometric factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques based on the deep interplay between algebra, differential geometry and topology. The book aims at being a guide to advanced differential geometric and topological methods in quantum mechanics. Their main peculiarity lies in the fact that geometry in quantum theory speaks mainly the algebraic language of rings, modules, sheaves and categories. Geometry is by no means the primary scope of the book, but it underlies many ideas in modern quantum physics and provides the most advanced schemes of quantization.
Quantum Geometry
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Author : Jan Ambjørn
language : en
Publisher: Cambridge University Press
Release Date : 1997-06-19
Quantum Geometry written by Jan Ambjørn and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06-19 with Science categories.
Describes random geometry and applications to strings, quantum gravity, topological field theory and membrane physics.
Geometry Of Quantum States
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Author : Ingemar Bengtsson
language : en
Publisher: Cambridge University Press
Release Date : 2017-08-18
Geometry Of Quantum States written by Ingemar Bengtsson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-18 with Mathematics categories.
This new edition describes the space of quantum states and the theory of quantum entanglement from a geometric perspective.
Quantum Mechanics Quantum Field Theory
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Author : R. Mirman
language : en
Publisher: Nova Publishers
Release Date : 2001
Quantum Mechanics Quantum Field Theory written by R. Mirman and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Science categories.
Excision of errors and confusion about quantum mechanics -- and stimulation of thoughtful and adventurous readers are pre-eminent rationales of this entire work; these requiring definitions and analysis of underlying concepts of quantum mechanics, of quantum field theory -- why probability is given by the absolute square, what wavefunctions are and are not and why, and many others -- and also examination of some from the philosophy of science. People's beliefs about quantum mechanics are often just the reverse of what fundamental principles give, seen most spectacularly with the EPR 'paradox'. The puzzles, the mystical, the bizarre, come merely from negligence, from blunders, including the outlandish belief that the universe must be explained using classical physics. Careless, unthinking physicists, and gullible journalists who naively accept their confusion as statements about nature, cause so much misunderstanding and nonsense about physics. Among the many examples considered are the non-existence in quantum mechanics of waves and particles, so of wave-particle duality; the reason that general relativity must be the quantum theory of gravity; the mystery of the cosmological constant: why people believe in it though it would be obvious to a high school student that there cannot be any, it must be zero; the absurdity (and wild incorrectness) of much of the discussion about the vacuum; the required locality of quantum mechanics and the impossibility of action-at-a-distance; and many others. Many blunders, not only about physics, come from abuse of language, the use of words, phrases, sentences without content, with con- notation but no denotation, of names --- quantum mechanics, particles, waves, and so on -- that deceive and misrepresent, of questions that ask nothing. It is not only in physics that answers to questions without meaning smother and hide.
Quantum Mechanics Built On Algebraic Geometry
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Author : Akihito Kikuchi
language : en
Publisher:
Release Date : 2021-01-04
Quantum Mechanics Built On Algebraic Geometry written by Akihito Kikuchi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-04 with categories.
This book presents a novel standpoint concerning contemporary physics, namely, quantum mechanics with a view toward algebraic geometry. As is well-known, algebraic geometry is the study of geometric objects delineated by polynomials, and the polynomial representations are ubiquitous in physics. For this reason, quantum mechanics is also an object of algebraic geometry. An example is the eigenvalue problem. It is a set of polynomial equations and has traditionally been the question of linear algebra. However, the modern method of computational algebraic geometry accurately unravels the information encapsulated in the polynomials. This approach shall not remain as a plaything. It has betokened an innovative style of electronic structure computation. The objects of this new method include the simultaneous determination of the wave-functions and the movements of nuclei, or the prediction of the required structure that shall show the desired property. Accordingly, this book explains the basic ideas of computational algebraic geometry and related topics, such as Groebner bases, primary ideal decomposition, Dmodules, Galois, class field theory, etc. The intention of the author is, nevertheless, not to give an irksome list of abstract concepts. He hopes that the readers shall use algebraic geometry as the active tool of the computations. For this reason, this book abundantly presents the model computations, by which the readers shall learn how to apply algebraic geometry toward quantum mechanics. The readers shall also see the modern computer algebra could facilitate the study when you would like to apply abstract mathematical ideas to definite physical problems.