Quantum Theories And Geometry

Author : Edoardo Ballico,Alessandra Bernardi,Iacopo Carusotto,Sonia Mazzucchi,Valter Moretti
Publisher : Springer
Page : 173 pages
File Size : 55,8 Mb
Release : 2019-03-13
Category : Science
ISBN : 9783030061227

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Quantum Physics and Geometry by Edoardo Ballico,Alessandra Bernardi,Iacopo Carusotto,Sonia Mazzucchi,Valter Moretti Pdf

This book collects independent contributions on current developments in quantum information theory, a very interdisciplinary field at the intersection of physics, computer science and mathematics. Making intense use of the most advanced concepts from each discipline, the authors give in each contribution pedagogical introductions to the main concepts underlying their present research and present a personal perspective on some of the most exciting open problems. Keeping this diverse audience in mind, special efforts have been made to ensure that the basic concepts underlying quantum information are covered in an understandable way for mathematical readers, who can find there new open challenges for their research. At the same time, the volume can also be of use to physicists wishing to learn advanced mathematical tools, especially of differential and algebraic geometric nature.

Author : V.S. Varadarajan
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 44,8 Mb
Release : 2007-12-03
Category : Science
ISBN : 9780387493862

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Geometry of Quantum Theory by V.S. Varadarajan Pdf

Available for the first time in soft cover, this book is a classic on the foundations of quantum theory. It examines the subject from a point of view that goes back to Heisenberg and Dirac and whose definitive mathematical formulation is due to von Neumann. This view leads most naturally to the fundamental questions that are at the basis of all attempts to understand the world of atomic and subatomic particles.

Author : Maurice A. de Gosson
Publisher : Springer Science & Business Media
Page : 375 pages
File Size : 45,9 Mb
Release : 2006-08-06
Category : Mathematics
ISBN : 9783764375751

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Symplectic Geometry and Quantum Mechanics by Maurice A. de Gosson Pdf

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.

Author : Veeravalli S. Varadarajan
Publisher : Unknown
Page : 255 pages
File Size : 40,7 Mb
Release : 1970
Category : Electronic
ISBN : OCLC:174919096

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Geometry of Quantum Theory by Veeravalli S. Varadarajan Pdf

Author : Roger Boudet
Publisher : Springer Science & Business Media
Page : 126 pages
File Size : 47,6 Mb
Release : 2011-06-13
Category : Science
ISBN : 9783642191992

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Quantum Mechanics in the Geometry of Space-Time by Roger Boudet Pdf

This book continues the fundamental work of Arnold Sommerfeld and David Hestenes formulating theoretical physics in terms of Minkowski space-time geometry. We see how the standard matrix version of the Dirac equation can be reformulated in terms of a real space-time algebra, thus revealing a geometric meaning for the “number i” in quantum mechanics. Next, it is examined in some detail how electroweak theory can be integrated into the Dirac theory and this way interpreted in terms of space-time geometry. Finally, some implications for quantum electrodynamics are considered. The presentation of real quantum electromagnetism is expressed in an addendum. The book covers both the use of the complex and the real languages and allows the reader acquainted with the first language to make a step by step translation to the second one.

Author : Margaret Prugovecki
Publisher : Springer Science & Business Media
Page : 543 pages
File Size : 49,6 Mb
Release : 2013-03-14
Category : Science
ISBN : 9789401579711

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Quantum Geometry by Margaret Prugovecki Pdf

This monograph presents a review and analysis of the main mathematical, physical and epistomological difficulties encountered at the foundational level by all the conventional formulations of relativistic quantum theories, ranging from relativistic quantum mechanics and quantum field theory in Minkowski space, to the various canonical and covariant approaches to quantum gravity. It is, however, primarily devoted to the systematic presentation of a quantum framework meant to deal effectively with these difficulties by reconsidering the foundations of these subjects, analyzing their epistemic nature, and then developing mathematical tools which are specifically designed for the elimination of all the basic inconsistencies. A carefully documented historical survey is included, and additional extensive notes containing quotations from original sources are incorporated at the end of each chapter, so that the reader will be brought up-to-date with the very latest developments in quantum field theory in curved spacetime, quantum gravity and quantum cosmology. The survey further provides a backdrop against which the new foundational and mathematical ideas of the present approach to these subjects can be brought out in sharper relief.

Author : Kai S Lam
Publisher : World Scientific Publishing Company
Page : 460 pages
File Size : 44,6 Mb
Release : 2009-08-24
Category : Science
ISBN : 9789813107489

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Non-Relativistic Quantum Theory by Kai S Lam Pdf

This textbook is mainly for physics students at the advanced undergraduate and beginning graduate levels, especially those with a theoretical inclination. Its chief purpose is to give a systematic introduction to the main ingredients of the fundamentals of quantum theory, with special emphasis on those aspects of group theory (spacetime and permutational symmetries and group representations) and differential geometry (geometrical phases, topological quantum numbers, and Chern–Simons Theory) that are relevant in modern developments of the subject. It will provide students with an overview of key elements of the theory, as well as a solid preparation in calculational techniques.

Author : M. Cahen,M. Flato
Publisher : Springer Science & Business Media
Page : 196 pages
File Size : 43,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400930551

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Quantum Theories and Geometry by M. Cahen,M. Flato Pdf

This book presents the text of most of the lectures which were de livered at the Meeting Quantum Theories and Geometry which was held at the Fondation Les Treilles from March 23 to March 27, 1987. The general aim of this meeting was to bring together mathemati cians and physicists who have worked in this growing field of contact between the two disciplines, namely this region where geometry and physics interact creatively in both directions. It 1S the strong belief of the organizers that these written con tributions will be a useful document for research people workin~ 1n geometry or physics. Three lectures were devoted to the deformation approach to quantum mechanics which involves a modification of both the associative and the Lie structure of the algebra of functions on classical phase space. A. Lichnerowicz shows how one can view classical and quantum statistical mechanics in terms of a deformation with a parameter inversely propor tional to temperature. S. Gutt reviews the physical background of star products and indicates their applications in Lie groups representa tion theory and in harmonic analysis. D. Arnal gives a rigorous theory Vll viii PREFACI of the star exponential in the case of the Heisenberg group and shows how this can be extended to arbitrary nilpotent groups.

Author : Luigi Mangiarotti,Gennadi A Sardanashvily,Giovanni Giachetta
Publisher : World Scientific
Page : 715 pages
File Size : 46,6 Mb
Release : 2005-01-27
Category : Science
ISBN : 9789814481144

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Geometric And Algebraic Topological Methods In Quantum Mechanics by Luigi Mangiarotti,Gennadi A Sardanashvily,Giovanni Giachetta Pdf

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.

Author : Kieran Finn
Publisher : Springer Nature
Page : 212 pages
File Size : 48,6 Mb
Release : 2021-10-07
Category : Science
ISBN : 9783030852696

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Geometric Approaches to Quantum Field Theory by Kieran Finn Pdf

The ancient Greeks believed that everything in the Universe should be describable in terms of geometry. This thesis takes several steps towards realising this goal by introducing geometric descriptions of systems such as quantum gravity, fermionic particles and the origins of the Universe itself. The author extends the applicability of previous work by Vilkovisky, DeWitt and others to include theories with spin 1⁄2 and spin 2 degrees of freedom. In addition, he introduces a geometric description of the potential term in a quantum field theory through a process known as the Eisenhart lift. Finally, the methods are applied to the theory of inflation, where they show how geometry can help answer a long-standing question about the initial conditions of the Universe. This publication is aimed at graduate and advanced undergraduate students and provides a pedagogical introduction to the exciting topic of field space covariance and the complete geometrization of quantum field theory.

Author : R. Mirman
Publisher : iUniverse
Page : 341 pages
File Size : 47,6 Mb
Release : 2004-12
Category : Quantum field theory
ISBN : 9780595336906

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Quantum Mechanics, Quantum Field Theory by R. Mirman Pdf

The author does not want a book description on the back cover.

Author : Jedrzej Sniatycki
Publisher : Springer Science & Business Media
Page : 241 pages
File Size : 41,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461260660

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Geometric Quantization and Quantum Mechanics by Jedrzej Sniatycki Pdf

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.

Author : Daniel S. Freed,Karen K. Uhlenbeck,American Mathematical Society,Institute for Advanced Study (Princeton, N.J.)
Publisher : American Mathematical Soc.
Page : 476 pages
File Size : 45,6 Mb
Release : 1995
Category : Science
ISBN : 0821886835

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Geometry and Quantum Field Theory by Daniel S. Freed,Karen K. Uhlenbeck,American Mathematical Society,Institute for Advanced Study (Princeton, N.J.) Pdf

The first title in a new series, this book explores topics from classical and quantum mechanics and field theory. The material is presented at a level between that of a textbook and research papers making it ideal for graduate students. The book provides an entree into a field that promises to remain exciting and important for years to come.

Author : Dariusz Chruscinski,Andrzej Jamiolkowski
Publisher : Springer Science & Business Media
Page : 337 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780817681760

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Geometric Phases in Classical and Quantum Mechanics by Dariusz Chruscinski,Andrzej Jamiolkowski Pdf

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.

Author : Jan Ambjørn,Bergfinnur Durhuus,Þórður Jónsson
Publisher : Cambridge University Press
Page : 377 pages
File Size : 44,8 Mb
Release : 1997-06-19
Category : Science
ISBN : 9780521461672

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Quantum Geometry by Jan Ambjørn,Bergfinnur Durhuus,Þórður Jónsson Pdf

Describes random geometry and applications to strings, quantum gravity, topological field theory and membrane physics.