Geometrical Quantum Mechanics
Geometrical Quantum Mechanics

Author: Robert Geroch

Publisher: Minkowski Institute Press

Published: 2013-03-23

Total Pages: 137

ISBN-13: 1927763045

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Geroch's lecture notes on geometrical quantum mechanics are divided into three parts - Differential Geometry, Mechanics, and Quantum Mechanics. The necessary geometrical ideas are presented in the first part of the book and are applied to mechanics and quantum mechanics in the second and third part. What also makes this book a valuable contribution to the existing textbooks on quantum physics is Geroch's unique approach to teaching theoretical and mathematical physics - the physical concepts and the mathematics, which describes them, are masterfully intertwined in such a way that both reinforce each other to facilitate the understanding of even the most abstract and subtle issues.

Geometric Formulation of Classical and Quantum Mechanics
Geometric Formulation of Classical and Quantum Mechanics

Author: G. Giachetta

Publisher: World Scientific

Published: 2011

Total Pages: 405

ISBN-13: 9814313726

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The geometric formulation of autonomous Hamiltonian mechanics in the terms of symplectic and Poisson manifolds is generally accepted. This book provides the geometric formulation of non-autonomous mechanics in a general setting of time-dependent coordinate and reference frame transformations.

Quantum Physics and Geometry
Quantum Physics and Geometry

Author: Edoardo Ballico

Publisher: Springer

Published: 2019-03-13

Total Pages: 177

ISBN-13: 3030061221

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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.

Symplectic Geometry and Quantum Mechanics
Symplectic Geometry and Quantum Mechanics

Author: Maurice A. de Gosson

Publisher: Springer Science & Business Media

Published: 2006-08-06

Total Pages: 375

ISBN-13: 3764375752

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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.

Geometric Phases in Classical and Quantum Mechanics
Geometric Phases in Classical and Quantum Mechanics

Author: Dariusz Chruscinski

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 346

ISBN-13: 0817681760

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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.

Geometric Quantization and Quantum Mechanics
Geometric Quantization and Quantum Mechanics

Author: Jedrzej Sniatycki

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 241

ISBN-13: 1461260663

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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 in the Geometry of Space-Time
Quantum Mechanics in the Geometry of Space-Time

Author: Roger Boudet

Publisher: Springer Science & Business Media

Published: 2011-06-13

Total Pages: 126

ISBN-13: 3642191991

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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.

Quantum Geometry
Quantum Geometry

Author: Jan Ambjørn

Publisher: Cambridge University Press

Published: 1997-06-19

Total Pages: 377

ISBN-13: 0521461677

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

Geometry and Quantum Field Theory
Geometry and Quantum Field Theory

Author: Daniel S. Freed

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 476

ISBN-13: 9780821886830

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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.