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Quantum Physics and Geometry

Author : Edoardo Ballico

Publisher : Springer

Page : 173 pages

File Size : 36,78 MB

Release : 2019-03-13

Category : Science

ISBN : 3030061221

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Book Description

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

Author : Margaret Prugovecki

Publisher : Springer Science & Business Media

Page : 543 pages

File Size : 18,53 MB

Release : 2013-03-14

Category : Science

ISBN : 9401579717

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Book Description

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.



Geometric Phases in Classical and Quantum Mechanics

Author : Dariusz Chruscinski

Publisher : Springer Science & Business Media

Page : 346 pages

File Size : 33,15 MB

Release : 2012-12-06

Category : Mathematics

ISBN : 0817681760

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Book Description

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

Author : Maurice A. de Gosson

Publisher : Springer Science & Business Media

Page : 375 pages

File Size : 31,82 MB

Release : 2006-08-06

Category : Mathematics

ISBN : 3764375752

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Book Description

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

Author : Ingemar Bengtsson

Publisher : Cambridge University Press

Page : 637 pages

File Size : 38,46 MB

Release : 2017-08-18

Category : Science

ISBN : 1108293492

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Book Description

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.



Geometric Quantization and Quantum Mechanics

Author : Jedrzej Sniatycki

Publisher : Springer Science & Business Media

Page : 241 pages

File Size : 29,81 MB

Release : 2012-12-06

Category : Science

ISBN : 1461260663

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Book Description

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 Geometry

Author : Jan Ambjørn

Publisher : Cambridge University Press

Page : 377 pages

File Size : 14,87 MB

Release : 1997-06-19

Category : Science

ISBN : 0521461677

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Book Description

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



Geometric and Topological Methods for Quantum Field Theory

Author : Hernan Ocampo

Publisher : Cambridge University Press

Page : 435 pages

File Size : 43,43 MB

Release : 2010-04-29

Category : Science

ISBN : 113948673X

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Book Description

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 Mechanics in the Geometry of Space-Time

Author : Roger Boudet

Publisher : Springer Science & Business Media

Page : 126 pages

File Size : 35,86 MB

Release : 2011-06-13

Category : Science

ISBN : 3642191991

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Book Description

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.