Geometry of Quantum Theory
Author : Veeravalli S. Varadarajan
Publisher :
Page : 255 pages
File Size : 29,63 MB
Release : 1970
Category :
ISBN :
Quantum Physics and Geometry
Author : Edoardo Ballico
Publisher : Springer
Page : 177 pages
File Size : 42,6 MB
Release : 2019-03-13
Category : Science
ISBN : 3030061221
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.
Geometry of Quantum States
Author : Ingemar Bengtsson
Publisher : Cambridge University Press
Page : 637 pages
File Size : 46,57 MB
Release : 2017-08-18
Category : Science
ISBN : 1108293492
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.
Geometry and Quantum Field Theory
Author : Daniel S. Freed
Publisher : American Mathematical Soc.
Page : 476 pages
File Size : 40,72 MB
Release : 1995
Category : Science
ISBN : 9780821886830
Book Description
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
Author : Maurice A. de Gosson
Publisher : Springer Science & Business Media
Page : 375 pages
File Size : 21,38 MB
Release : 2006-08-06
Category : Mathematics
ISBN : 3764375752
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.
Quantum Geometry
Author : Margaret Prugovecki
Publisher : Springer Science & Business Media
Page : 543 pages
File Size : 26,36 MB
Release : 2013-03-14
Category : Science
ISBN : 9401579717
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.
Quantum Geometry
Author : Jan Ambjørn
Publisher : Cambridge University Press
Page : 377 pages
File Size : 12,3 MB
Release : 1997-06-19
Category : Science
ISBN : 0521461677
Book Description
Describes random geometry and applications to strings, quantum gravity, topological field theory and membrane physics.
Operators, Geometry and Quanta
Author : Dmitri Fursaev
Publisher : Springer Science & Business Media
Page : 294 pages
File Size : 20,57 MB
Release : 2011-06-25
Category : Science
ISBN : 9400702051
Book Description
This book gives a detailed and self-contained introduction into the theory of spectral functions, with an emphasis on their applications to quantum field theory. All methods are illustrated with applications to specific physical problems from the forefront of current research, such as finite-temperature field theory, D-branes, quantum solitons and noncommutativity. In the first part of the book, necessary background information on differential geometry and quantization, including less standard material, is collected. The second part of the book contains a detailed description of main spectral functions and methods of their calculation. In the third part, the theory is applied to several examples (D-branes, quantum solitons, anomalies, noncommutativity). This book addresses advanced graduate students and researchers in mathematical physics with basic knowledge of quantum field theory and differential geometry. The aim is to prepare readers to use spectral functions in their own research, in particular in relation to heat kernels and zeta functions.
Geometric Phases in Classical and Quantum Mechanics
Author : Dariusz Chruscinski
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 39,31 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 0817681760
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.
Geometric and Topological Methods for Quantum Field Theory
Author : Sylvie Paycha
Publisher : American Mathematical Soc.
Page : 272 pages
File Size : 36,79 MB
Release : 2007
Category : Mathematics
ISBN : 0821840622
Book Description
This volume, based on lectures and short communications at a summer school in Villa de Leyva, Colombia (July 2005), offers an introduction to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. It is aimed at graduate students in physics or mathematics who might want insight in the following topics (covered in five survey lectures): Anomalies and noncommutative geometry, Deformation quantisation and Poisson algebras, Topological quantum field theory and orbifolds. These lectures are followed by nine articles on various topics at the borderline of mathematics and physics ranging from quasicrystals to invariant instantons through black holes, and involving a number of mathematical tools borrowed from geometry, algebra and analysis.
