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The Theory Of Symmetry Actions In Quantum Mechanics

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The Theory Of Symmetry Actions In Quantum Mechanics

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Author : Gianni Cassinelli
language : en
Publisher: Springer
Release Date : 2014-03-12

The Theory Of Symmetry Actions In Quantum Mechanics written by Gianni Cassinelli and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-12 with Science categories.

This is a book about representing symmetry in quantum mechanics. The book is on a graduate and/or researcher level and it is written with an attempt to be concise, to respect conceptual clarity and mathematical rigor. The basic structures of quantum mechanics are used to identify the automorphism group of quantum mechanics. The main concept of a symmetry action is defined as a group homomorphism from a given group, the group of symmetries, to the automorphism group of quantum mechanics. The structure of symmetry actions is determined under the assumption that the symmetry group is a Lie group. The Galilei invariance is used to illustrate the general theory by giving a systematic presentation of a Galilei invariant elementary particle. A brief description of the Galilei invariant wave equations is also given.

The Theory Of Symmetry Actions In Quantum Mechanics

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Author :
language : en
Publisher:
Release Date : 2004

The Theory Of Symmetry Actions In Quantum Mechanics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Quantum theory categories.

The Theory Of Symmetry Actions In Quantum Mechanics

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Author : Gianni Cassinelli
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-10-27

The Theory Of Symmetry Actions In Quantum Mechanics written by Gianni Cassinelli 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 2004-10-27 with Science categories.

Spectral Theory And Quantum Mechanics

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Author : Valter Moretti
language : en
Publisher: Springer
Release Date : 2018-01-30

Spectral Theory And Quantum Mechanics written by Valter Moretti and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-30 with Mathematics categories.

This book discusses the mathematical foundations of quantum theories. It offers an introductory text on linear functional analysis with a focus on Hilbert spaces, highlighting the spectral theory features that are relevant in physics. After exploring physical phenomenology, it then turns its attention to the formal and logical aspects of the theory. Further, this Second Edition collects in one volume a number of useful rigorous results on the mathematical structure of quantum mechanics focusing in particular on von Neumann algebras, Superselection rules, the various notions of Quantum Symmetry and Symmetry Groups, and including a number of fundamental results on the algebraic formulation of quantum theories. Intended for Master's and PhD students, both in physics and mathematics, the material is designed to be self-contained: it includes a summary of point-set topology and abstract measure theory, together with an appendix on differential geometry. The book also benefits established researchers by organizing and presenting the profusion of advanced material disseminated in the literature. Most chapters are accompanied by exercises, many of which are solved explicitly."

Lectures On The Mathematics Of Quantum Mechanics Ii Selected Topics

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Author : Gianfausto Dell'Antonio
language : en
Publisher: Springer
Release Date : 2016-05-24

Lectures On The Mathematics Of Quantum Mechanics Ii Selected Topics written by Gianfausto Dell'Antonio and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-24 with Science categories.

The first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part (Selected Topics) are lecture notes of a more advanced course aimed at giving the basic notions necessary to do research in several areas of mathematical physics connected with quantum mechanics, from solid state to singular interactions, many body theory, semi-classical analysis, quantum statistical mechanics. The structure of this book is suitable for a second-semester course, in which the lectures are meant to provide, in addition to theorems and proofs, an overview of a more specific subject and hints to the direction of research. In this respect and for the width of subjects this second volume differs from other monographs on Quantum Mechanics. The second volume can be useful for students who want to have a basic preparation for doing research and for instructors who may want to use it as a basis for the presentation of selected topics.

Quantum Mechanics Mathematics Cognition And Action

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Author : Mioara Mugur-Schächter
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-11

Quantum Mechanics Mathematics Cognition And Action written by Mioara Mugur-Schächter 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 2006-04-11 with Science categories.

And starting from there, it can induce an explicit understanding of certain fundamental features of the new scientific thinking. A formalized epistemology should not be mistaken for a crossdisciplinary or a multidisciplinary project. The latter projects are designed to offer to nonspecialists access to information, to results obtained inside specialized disciplines, as well as a certain understanding of these results; whereas a formalized epistemology should equip anyone with a framework for conceptualizing himself in whatever domain and direction he or she might choose. A formalized epistemology should not be mistaken either for an approach belonging to the modern cognitive sciences

The Feynman Integral And Feynman S Operational Calculus

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Author :
language : en
Publisher: OUP Oxford
Release Date : 2000-03-16

The Feynman Integral And Feynman S Operational Calculus written by and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-03-16 with Mathematics categories.

The aim of this book is to make accessible to mathematicians, physicists and other scientists interested in qunatum theory, the beautiful but mathematically difficult subjects of the Feynman integral and Feynman's operational calculus. Some advantages of the approaches to the Feynman integral which are treated in detail in this book are the following: the existence of the Feynman integral is established for very general potentials in all four cases; under more restrictive but still broad conditions, three of these Feynman integrals agree with one another and with the unitary group from the usual approach to quantum dynamics; these same three Feynman integrals possess pleasant stability properties. Much of the material covered here was previously available only in the research literature, and the book also contains some new results. The background material in mathematics and physics that motivates the study of the Feynman integral and Feynman's operational calculus is discussed, and detailed proofs are provided for the central results.

Reflections On Quanta Symmetries And Supersymmetries

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Author : V.S. Varadarajan
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-20

Reflections On Quanta Symmetries And Supersymmetries written by V.S. Varadarajan 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 2011-05-20 with Mathematics categories.

This is a collection of essays based on lectures that author has given on various occasions on foundation of quantum theory, symmetries and representation theory, and the quantum theory of the superworld created by physicists. The lectures are linked by a unifying theme: how the quantum world and superworld appear under the lens of symmetry and supersymmetry. In the world of ultra-small times and distances such as the Planck length and Planck time, physicists believe no measurements are possible and so the structure of spacetime itself is an unknown that has to be first understood. There have been suggestions (Volovich hypothesis) that world geometry at such energy regimes is non-archimedian and some of the lectures explore the consequences of such a hypothesis. Ultimately, symmetries and supersymmetries are described by the representation of groups and supergroups. The author's interest in representation is a lifelong one and evolved slowly, and owes a great deal to conversations and discussions he had with George Mackey and Harish-Chandra. The book concludes with a retrospective look at these conversations.

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.

Conceptual Foundations Of Quantum Field Theory

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Author : Tian Yu Cao
language : en
Publisher: Cambridge University Press
Release Date : 2004-03-25

Conceptual Foundations Of Quantum Field Theory written by Tian Yu Cao 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 2004-03-25 with Science categories.

Multi-author volume on the history and philosophy of physics.

The Theory Of Symmetry Actions In Quantum Mechanics

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