Quantum Physics and Geometry

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Publisher : Springer
ISBN 13 : 3030061221
Total Pages : 173 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Quantum Physics and Geometry by : Edoardo Ballico

Download or read book Quantum Physics and Geometry written by Edoardo Ballico and published by Springer. This book was released on 2019-03-13 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Quantum Geometry

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Publisher : Springer Science & Business Media
ISBN 13 : 9401579717
Total Pages : 543 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Quantum Geometry by : Margaret Prugovecki

Download or read book Quantum Geometry written by Margaret Prugovecki and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometry of Quantum Theory

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Publisher :
ISBN 13 :
Total Pages : 255 pages
Book Rating : 4.:/5 (174 download)

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Book Synopsis Geometry of Quantum Theory by : Veeravalli S. Varadarajan

Download or read book Geometry of Quantum Theory written by Veeravalli S. Varadarajan and published by . This book was released on 1970 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Geometric Phases in Classical and Quantum Mechanics

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Publisher : Springer Science & Business Media
ISBN 13 : 0817681760
Total Pages : 337 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Geometric Phases in Classical and Quantum Mechanics by : Dariusz Chruscinski

Download or read book Geometric Phases in Classical and Quantum Mechanics written by Dariusz Chruscinski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Symplectic Geometry and Quantum Mechanics

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Publisher : Springer Science & Business Media
ISBN 13 : 3764375752
Total Pages : 375 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Symplectic Geometry and Quantum Mechanics by : Maurice A. de Gosson

Download or read book Symplectic Geometry and Quantum Mechanics written by Maurice A. de Gosson and published by Springer Science & Business Media. This book was released on 2006-08-06 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometry of Quantum States

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Publisher : Cambridge University Press
ISBN 13 : 1108293492
Total Pages : 637 pages
Book Rating : 4.1/5 (82 download)

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Book Synopsis Geometry of Quantum States by : Ingemar Bengtsson

Download or read book Geometry of Quantum States written by Ingemar Bengtsson and published by Cambridge University Press. This book was released on 2017-08-18 with total page 637 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum information theory is a branch of science at the frontier of physics, mathematics, and information science, and offers a variety of solutions that are impossible using classical theory. This book provides a detailed introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory. The second edition contains new sections and entirely new chapters: the hot topic of multipartite entanglement; in-depth discussion of the discrete structures in finite dimensional Hilbert space, including unitary operator bases, mutually unbiased bases, symmetric informationally complete generalized measurements, discrete Wigner function, and unitary designs; the Gleason and Kochen–Specker theorems; the proof of the Lieb conjecture; the measure concentration phenomenon; and the Hastings' non-additivity theorem. This richly-illustrated book will be useful to a broad audience of graduates and researchers interested in quantum information theory. Exercises follow each chapter, with hints and answers supplied.

Geometry and Quantum Field Theory

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821886830
Total Pages : 476 pages
Book Rating : 4.8/5 (868 download)

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Book Synopsis Geometry and Quantum Field Theory by : Daniel S. Freed

Download or read book Geometry and Quantum Field Theory written by Daniel S. Freed and published by American Mathematical Soc.. This book was released on 1995 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Non-Relativistic Quantum Theory

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Publisher : World Scientific Publishing Company
ISBN 13 : 9813107480
Total Pages : 460 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Non-Relativistic Quantum Theory by : Kai S Lam

Download or read book Non-Relativistic Quantum Theory written by Kai S Lam and published by World Scientific Publishing Company. This book was released on 2009-08-24 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometric Approaches to Quantum Field Theory

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Publisher : Springer Nature
ISBN 13 : 3030852695
Total Pages : 212 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Geometric Approaches to Quantum Field Theory by : Kieran Finn

Download or read book Geometric Approaches to Quantum Field Theory written by Kieran Finn and published by Springer Nature. This book was released on 2021-10-07 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometry of Quantum Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 0387493867
Total Pages : 426 pages
Book Rating : 4.3/5 (874 download)

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Book Synopsis Geometry of Quantum Theory by : V.S. Varadarajan

Download or read book Geometry of Quantum Theory written by V.S. Varadarajan and published by Springer Science & Business Media. This book was released on 2007-12-03 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometric and Topological Methods for Quantum Field Theory

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Publisher : Cambridge University Press
ISBN 13 : 113948673X
Total Pages : 435 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Geometric and Topological Methods for Quantum Field Theory by : Hernan Ocampo

Download or read book Geometric and Topological Methods for Quantum Field Theory written by Hernan Ocampo and published by Cambridge University Press. This book was released on 2010-04-29 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at graduate students in physics and mathematics, this book provides an introduction to recent developments in several active topics at the interface between algebra, geometry, topology and quantum field theory. The first part of the book begins with an account of important results in geometric topology. It investigates the differential equation aspects of quantum cohomology, before moving on to noncommutative geometry. This is followed by a further exploration of quantum field theory and gauge theory, describing AdS/CFT correspondence, and the functional renormalization group approach to quantum gravity. The second part covers a wide spectrum of topics on the borderline of mathematics and physics, ranging from orbifolds to quantum indistinguishability and involving a manifold of mathematical tools borrowed from geometry, algebra and analysis. Each chapter presents introductory material before moving on to more advanced results. The chapters are self-contained and can be read independently of the rest.

Quantum Geometry

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Publisher : Cambridge University Press
ISBN 13 : 0521461677
Total Pages : 377 pages
Book Rating : 4.5/5 (214 download)

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Book Synopsis Quantum Geometry by : Jan Ambjørn

Download or read book Quantum Geometry written by Jan Ambjørn and published by Cambridge University Press. This book was released on 1997-06-19 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes random geometry and applications to strings, quantum gravity, topological field theory and membrane physics.

Geometric And Algebraic Topological Methods In Quantum Mechanics

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Publisher : World Scientific
ISBN 13 : 9814481149
Total Pages : 715 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Geometric And Algebraic Topological Methods In Quantum Mechanics by : Luigi Mangiarotti

Download or read book Geometric And Algebraic Topological Methods In Quantum Mechanics written by Luigi Mangiarotti and published by World Scientific. This book was released on 2005-01-27 with total page 715 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometric Quantization and Quantum Mechanics

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Publisher : Springer Science & Business Media
ISBN 13 : 1461260663
Total Pages : 241 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Geometric Quantization and Quantum Mechanics by : Jedrzej Sniatycki

Download or read book Geometric Quantization and Quantum Mechanics written by Jedrzej Sniatycki and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Quantum Mechanics of Particles and Wave Fields

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Publisher : Courier Corporation
ISBN 13 : 048644578X
Total Pages : 308 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Quantum Mechanics of Particles and Wave Fields by : Arthur March

Download or read book Quantum Mechanics of Particles and Wave Fields written by Arthur March and published by Courier Corporation. This book was released on 2006-01-01 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete explanation of quantum mechanics, from its early non-relativistic formulation to the complex field theories used so extensively in modern theoretical research, this volume assumes no specialized knowledge of the subject. It stresses relativistic quantum mechanics, since this subject plays such an important role in research, explaining the principles clearly and imparting an accurate understanding of abstract concepts. This text deals with quantum mechanics from its earliest developments, covering both the quantum mechanics of wave fields and the older quantum theory of particles. The final chapter culminates with the author's presentation of his revolutionary theory of fundamental length--a concept designed to meet many of quantum theory's longstanding basic difficulties.

Instanton Counting, Quantum Geometry and Algebra

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Publisher : Springer Nature
ISBN 13 : 3030761908
Total Pages : 297 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Instanton Counting, Quantum Geometry and Algebra by : Taro Kimura

Download or read book Instanton Counting, Quantum Geometry and Algebra written by Taro Kimura and published by Springer Nature. This book was released on 2021-07-05 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book pedagogically describes recent developments in gauge theory, in particular four-dimensional N = 2 supersymmetric gauge theory, in relation to various fields in mathematics, including algebraic geometry, geometric representation theory, vertex operator algebras. The key concept is the instanton, which is a solution to the anti-self-dual Yang–Mills equation in four dimensions. In the first part of the book, starting with the systematic description of the instanton, how to integrate out the instanton moduli space is explained together with the equivariant localization formula. It is then illustrated that this formalism is generalized to various situations, including quiver and fractional quiver gauge theory, supergroup gauge theory. The second part of the book is devoted to the algebraic geometric description of supersymmetric gauge theory, known as the Seiberg–Witten theory, together with string/M-theory point of view. Based on its relation to integrable systems, how to quantize such a geometric structure via the Ω-deformation of gauge theory is addressed. The third part of the book focuses on the quantum algebraic structure of supersymmetric gauge theory. After introducing the free field realization of gauge theory, the underlying infinite dimensional algebraic structure is discussed with emphasis on the connection with representation theory of quiver, which leads to the notion of quiver W-algebra. It is then clarified that such a gauge theory construction of the algebra naturally gives rise to further affinization and elliptic deformation of W-algebra.

Quantum Mechanics in the Geometry of Space-Time

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Publisher : Springer Science & Business Media
ISBN 13 : 3642191991
Total Pages : 126 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Quantum Mechanics in the Geometry of Space-Time by : Roger Boudet

Download or read book Quantum Mechanics in the Geometry of Space-Time written by Roger Boudet and published by Springer Science & Business Media. This book was released on 2011-06-13 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.