Quantum Symmetries
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Quantum Symmetries
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Author : Guillaume Aubrun
language : en
Publisher: Springer
Release Date : 2017-10-11
Quantum Symmetries written by Guillaume Aubrun and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-11 with Mathematics categories.
Providing an introduction to current research topics in functional analysis and its applications to quantum physics, this book presents three lectures surveying recent progress and open problems. A special focus is given to the role of symmetry in non-commutative probability, in the theory of quantum groups, and in quantum physics. The first lecture presents the close connection between distributional symmetries and independence properties. The second introduces many structures (graphs, C*-algebras, discrete groups) whose quantum symmetries are much richer than their classical symmetry groups, and describes the associated quantum symmetry groups. The last lecture shows how functional analytic and geometric ideas can be used to detect and to quantify entanglement in high dimensions. The book will allow graduate students and young researchers to gain a better understanding of free probability, the theory of compact quantum groups, and applications of the theory of Banach spaces to quantum information. The latter applications will also be of interest to theoretical and mathematical physicists working in quantum theory.
Quantum Symmetries
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Author : Alain Connes
language : en
Publisher: North-Holland
Release Date : 1998
Quantum Symmetries written by Alain Connes and has been published by North-Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Foreign Language Study categories.
Hardbound. One of the greatest challenges that theoretical physics faces at the end of the century is to blend together the two revolutions of the beginning of the century, namely general relativity and quantum mechanics. One message that has become clear from the start and is common to both revolutions is that there is no limit to the level of sophistication of mathematics that will become essential to physics. This book comprises the lecture notes of the 1995 Les Houches Summer School. The aim of the school was to cover a wide range of areas, from theoretical physics to abstract mathematics, that are relevant in the search of a quantum theory of gravity. The lectures provide a systematic introduction to topological and conformal field theories, supersymmetry and super Yang-Mills theories, string theory and superstring dualities, integrable lattice models and quantum groups, non commutative geometry and the theory of diffeomorphism groups.It is di
New Symmetry Principles In Quantum Field Theory
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Author : J. Frölich
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
New Symmetry Principles In Quantum Field Theory written by J. Frölich 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.
Soon after the discovery of quantum mechanics, group theoretical methods were used extensively in order to exploit rotational symmetry and classify atomic spectra. And until recently it was thought that symmetries in quantum mechanics should be groups. But it is not so. There are more general algebras, equipped with suitable structure, which admit a perfectly conventional interpretation as a symmetry of a quantum mechanical system. In any case, a "trivial representation" of the algebra is defined, and a tensor product of representations. But in contrast with groups, this tensor product needs to be neither commutative nor associative. Quantum groups are special cases, in which associativity is preserved. The exploitation of such "Quantum Symmetries" was a central theme at the Ad vanced Study Institute. Introductory lectures were presented to familiarize the participants with the al gebras which can appear as symmetries and with their properties. Some models of local field theories were discussed in detail which have some such symmetries, in par ticular conformal field theories and their perturbations. Lattice models provide many examples of quantum theories with quantum symmetries. They were also covered at the school. Finally, the symmetries which are the cause of the solubility of inte grable models are also quantum symmetries of this kind. Some such models and their nonlocal conserved currents were discussed.
Quantum Symmetries On Operator Algebras
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Author : David Emrys Evans
language : en
Publisher:
Release Date : 1998
Quantum Symmetries On Operator Algebras written by David Emrys Evans and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
In the last 20 years, the study of operator algebras has developed from a branch of functional analysis to a central field of mathematics with applications and connections with different areas in both pure mathematics (foliations, index theory, K-theory, cyclic homology, affine Kac--Moody algebras, quantum groups, low dimensional topology) and mathematical physics (integrable theories, statistical mechanics, conformal field theories and the string theories of elementary particles). The theory of operator algebras was initiated by von Neumann and Murray as a tool for studying group representations and as a framework for quantum mechanics, and has since kept in touch with its roots in physics as a framework for quantum statistical mechanics and the formalism of algebraic quantum field theory. However, in 1981, the study of operator algebras took a new turn with the introduction by Vaughan Jones of subfactor theory and remarkable connections were found with knot theory, 3-manifolds, quantum groups and integrable systems in statistical mechanics and conformal field theory. The purpose of this book, one of the first in the area, is to look at these combinatorial-algebraic developments from the perspective of operator algebras; to bring the reader to the frontline of research with the minimum of prerequisites from classical theory.
Symmetries In Quantum Physics
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Author : U. Fano
language : en
Publisher: Elsevier
Release Date : 1996-06-17
Symmetries In Quantum Physics written by U. Fano and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-06-17 with Science categories.
This text focuses on the physics of symmetries, developing symmetries and transformations through concrete physical examples and contexts rather than presenting the information axiomatically, mathematically, and abstractly. Readers are introduced gradually to advanced mathematical procedures, including the Wigner and Racah algebras and their applications to various symmetry groups. The book also includes some of the latest research on the use of non-invariance and non-compact groups in the consideration of relativistic and many-particle problems of atoms and nuclei. This book is an updated replacement for the text Irreducible Tensorial Sets (Academic Press, 1959). Parts A and B of the present book grew out of occasional lectures in the intervening decades at the University of Chicago, where it became neccessary to update or elaborate upon certain points. Part C has been built more recently to deal with innovations and new information in the field of mathematical physics. The book as a whole develops the subject of symmetry from a physical point of view, allowing students and researchers to gain new insight on their subject. This book can be used both as a text and as a reference by students and scientists in the field. Adapts and extends the earlier Irreducible Tensor Sets (Academic Press, 1959) to classroom use Extends to multi-particle systems and relativity Includes problems in each chapter for homework assignments Embraces the latest research on non-invariance groups
Quantum Mechanics
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Author : Walter Greiner
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Quantum Mechanics written by Walter Greiner 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.
Greiner's lectures, which underlie these volumes, are internationally noted for their clarity, their completeness and for the effort that he has devoted to making physics an integral whole; his enthusiasm for his science is contagious and shines through almost every page. These volumes represent only a part of a unique and Herculean effort to make all of theoretical physics accessible to the interested student. Beyond that, they are of enormous value to the professional physicist and to all others working with quantum phenomena. Again and again the reader will find that, after dipping into a particular volume to review a specific topic, he will end up browsing, caught up by often fascinating new insights and developments with which he had not previously been familiar. Having used a number of Greiner's volumes in their original German in my teaching and research at Yale, I welcome these new and revised English translations and would recommend them enthusiastically to anyone searching for a coherent overview of physics.
Quantum Symmetries Proceedings Of The International Workshop On Mathematical Physics
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Author : Heinz-dietrich Doebner
language : en
Publisher: World Scientific
Release Date : 1993-10-29
Quantum Symmetries Proceedings Of The International Workshop On Mathematical Physics written by Heinz-dietrich Doebner and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-10-29 with categories.
Quantum symmetry modelled through quantum group or its dual, quantum algebra, is a very active field of relevant physical and mathematical research stimulated often by physical intuition and with promising physical applications. This volume gives some information on the progress of this field during the years after the quantum group workshop in Clausthal 1989. Quantum symmetry is connected with very different approaches and views. The field is not yet coherent; there are different notions of quantum groups and of quantum algebras through algebraic deformations of groups and algebras. Hence its development has various directions following more special mathematical and physical interests.
Quantum Theory And Symmetries
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Author : M. B. Paranjape
language : en
Publisher: Springer Nature
Release Date : 2021
Quantum Theory And Symmetries written by M. B. Paranjape and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Electronic books categories.
This volume of the CRM Conference Series is based on a carefully refereed selection of contributions presented at the "11th International Symposium on Quantum Theory and Symmetries", held in Montreal, Canada from July 1-5, 2019. The main objective of the meeting was to share and make accessible new research and recent results in several branches of Theoretical and Mathematical Physics, including Algebraic Methods, Condensed Matter Physics, Cosmology and Gravitation, Integrability, Non-perturbative Quantum Field Theory, Particle Physics, Quantum Computing and Quantum Information Theory, and String/ADS-CFT. There was also a special session in honour of Decio Levi. The volume is divided into sections corresponding to the sessions held during the symposium, allowing the reader to appreciate both the homogeneity and the diversity of mathematical tools that have been applied in these subject areas. Several of the plenary speakers, who are internationally recognized experts in their fields, have contributed reviews of the main topics to complement the original contributions. .
Symmetries In Quantum Mechanics
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Author : M Chaichian
language : en
Publisher: CRC Press
Release Date : 2023-07-21
Symmetries In Quantum Mechanics written by M Chaichian and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-21 with Science categories.
Symmetries in Quantum Mechanics: From Angular Momentum to Supersymmetry (PBK) provides a thorough, didactic exposition of the role of symmetry, particularly rotational symmetry, in quantum mechanics. The bulk of the book covers the description of rotations (geometrically and group-theoretically) and their representations, and the quantum theory of angular momentum. Later chapters introduce more advanced topics such as relativistic theory, supersymmetry, anyons, fractional spin, and statistics. With clear, in-depth explanations, the book is ideal for use as a course text for postgraduate and advanced undergraduate students in physics and those specializing in theoretical physics. It is also useful for researchers looking for an accessible introduction to this important area of quantum theory.
Symmetries In Fundamental Physics
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Author : Kurt Sundermeyer
language : en
Publisher: Springer
Release Date : 2014-07-23
Symmetries In Fundamental Physics written by Kurt Sundermeyer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-23 with Science categories.
Over the course of the last century it has become clear that both elementary particle physics and relativity theories are based on the notion of symmetries. These symmetries become manifest in that the "laws of nature" are invariant under spacetime transformations and/or gauge transformations. The consequences of these symmetries were analyzed as early as in 1918 by Emmy Noether on the level of action functionals. Her work did not receive due recognition for nearly half a century, but can today be understood as a recurring theme in classical mechanics, electrodynamics and special relativity, Yang-Mills type quantum field theories, and in general relativity. As a matter of fact, as shown in this monograph, many aspects of physics can be derived solely from symmetry considerations. This substantiates the statement of E.P. Wigner "... if we knew all the laws of nature, or the ultimate Law of nature, the invariance properties of these laws would not furnish us new information." Thanks to Wigner we now also understand the implications of quantum physics and symmetry considerations: Poincare invariance dictates both the characteristic properties of particles (mass, spin, ...) and the wave equations of spin 0, 1/2, 1, ... objects. Further, the work of C.N. Yang and R. Mills reveals the consequences of internal symmetries as exemplified in the symmetry group of elementary particle physics. Given this pivotal role of symmetries it is thus not surprising that current research in fundamental physics is to a great degree motivated and inspired by considerations of symmetry. The treatment of symmetries in this monograph ranges from classical physics to now well-established theories of fundamental interactions, to the latest research on unified theories and quantum gravity.