Quantum Physics and Geometry

by Edoardo Ballico
Quantum Physics and Geometry
Author: Edoardo Ballico
Publisher: Springer
Total Pages: 177
Release: 2019-03-13
Genre: Science
ISBN: 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.

Geometry and Quantum Field Theory

by Daniel S. Freed
Geometry and Quantum Field Theory
Author: Daniel S. Freed
Publisher: American Mathematical Soc.
Total Pages: 476
Release: 1995
Genre: Science
ISBN: 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.

Symplectic Geometry and Quantum Mechanics

by Maurice A. de Gosson
Symplectic Geometry and Quantum Mechanics
Author: Maurice A. de Gosson
Publisher: Springer Science & Business Media
Total Pages: 375
Release: 2006-08-06
Genre: Mathematics
ISBN: 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.

Geometry of Quantum States

by Ingemar Bengtsson
Geometry of Quantum States
Author: Ingemar Bengtsson
Publisher: Cambridge University Press
Total Pages: 637
Release: 2017-08-18
Genre: Science
ISBN: 1108293492
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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.

Quantum Geometry

by Jan Ambjørn
Quantum Geometry
Author: Jan Ambjørn
Publisher: Cambridge University Press
Total Pages: 377
Release: 1997-06-19
Genre: Science
ISBN: 0521461677
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Describes random geometry and applications to strings, quantum gravity, topological field theory and membrane physics.

Quantum Geometry

by Margaret Prugovecki
Quantum Geometry
Author: Margaret Prugovecki
Publisher: Springer Science & Business Media
Total Pages: 543
Release: 2013-03-14
Genre: Science
ISBN: 9401579717
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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

by Dariusz Chruscinski
Geometric Phases in Classical and Quantum Mechanics
Author: Dariusz Chruscinski
Publisher: Springer Science & Business Media
Total Pages: 346
Release: 2012-12-06
Genre: Mathematics
ISBN: 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 Approaches to Quantum Field Theory

by Kieran Finn
Geometric Approaches to Quantum Field Theory
Author: Kieran Finn
Publisher: Springer Nature
Total Pages: 212
Release: 2021-10-07
Genre: Science
ISBN: 3030852695
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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.