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Author : Gabriel Nagy
Publisher :
ISBN 13 :
Total Pages : 264 pages
Book Rating : 4.:/5 (33 download)
Download or read book A Framework for Deformation Quantization written by Gabriel Nagy and published by . This book was released on 1992 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Alexander Cardona
Publisher : Springer
ISBN 13 : 3319654276
Total Pages : 347 pages
Book Rating : 4.3/5 (196 download)
Download or read book Quantization, Geometry and Noncommutative Structures in Mathematics and Physics written by Alexander Cardona and published by Springer. This book was released on 2017-10-26 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents various ongoing approaches to the vast topic of quantization, which is the process of forming a quantum mechanical system starting from a classical one, and discusses their numerous fruitful interactions with mathematics.The opening chapter introduces the various forms of quantization and their interactions with each other and with mathematics.A first approach to quantization, called deformation quantization, consists of viewing the Planck constant as a small parameter. This approach provides a deformation of the structure of the algebra of classical observables rather than a radical change in the nature of the observables. When symmetries come into play, deformation quantization needs to be merged with group actions, which is presented in chapter 2, by Simone Gutt.The noncommutativity arising from quantization is the main concern of noncommutative geometry. Allowing for the presence of symmetries requires working with principal fiber bundles in a non-commutative setup, where Hopf algebras appear naturally. This is the topic of chapter 3, by Christian Kassel. Nichols algebras, a special type of Hopf algebras, are the subject of chapter 4, by Nicolás Andruskiewitsch. The purely algebraic approaches given in the previous chapters do not take the geometry of space-time into account. For this purpose a special treatment using a more geometric point of view is required. An approach to field quantization on curved space-time, with applications to cosmology, is presented in chapter 5 in an account of the lectures of Abhay Ashtekar that brings a complementary point of view to non-commutativity.An alternative quantization procedure is known under the name of string theory. In chapter 6 its supersymmetric version is presented. Superstrings have drawn the attention of many mathematicians, due to its various fruitful interactions with algebraic geometry, some of which are described here. The remaining chapters discuss further topics, as the Batalin-Vilkovisky formalism and direct products of spectral triples.This volume addresses both physicists and mathematicians and serves as an introduction to ongoing research in very active areas of mathematics and physics at the border line between geometry, topology, algebra and quantum field theory.
Author : Gilles Halbout
Publisher : Walter de Gruyter
ISBN 13 : 3110866226
Total Pages : 244 pages
Book Rating : 4.1/5 (18 download)
Download or read book Deformation Quantization written by Gilles Halbout and published by Walter de Gruyter. This book was released on 2012-10-25 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains eleven refereed research papers on deformation quantization by leading experts in the respective fields. These contributions are based on talks presented on the occasion of the meeting between mathematicians and theoretical physicists held in Strasbourg in May 2001. Topics covered are: star-products over Poisson manifolds, quantization of Hopf algebras, index theorems, globalization and cohomological problems. Both the mathematical and the physical approach ranging from asymptotic quantum electrodynamics to operads and prop theory will be presented. Historical remarks and surveys set the results presented in perspective. Directed at research mathematicians and theoretical physicists as well as graduate students, the volume will give an overview of a field of research that has seen enourmous acticity in the last years, with new ties to many other areas of mathematics and physics.
Author : Marc Aristide Rieffel
Publisher : American Mathematical Soc.
ISBN 13 : 0821825755
Total Pages : 110 pages
Book Rating : 4.8/5 (218 download)
Download or read book Deformation Quantization for Actions of $R^d$ written by Marc Aristide Rieffel and published by American Mathematical Soc.. This book was released on 1993 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work describes a general construction of a deformation quantization for any Poisson bracket on a manifold which comes from an action of R ]d on that manifold. These deformation quantizations are strict, in the sense that the deformed product of any two functions is again a function and that there are corresponding involutions and operator norms. Many of the techniques involved are adapted from the theory of pseudo-differential operators. The construction is shown to have many favorable properties. A number of specific examples are described, ranging from basic ones such as quantum disks, quantum tori, and quantum spheres, to aspects of quantum groups.
Author : Nima Moshayedi
Publisher : Springer Nature
ISBN 13 : 303105122X
Total Pages : 345 pages
Book Rating : 4.0/5 (31 download)
Download or read book Kontsevich’s Deformation Quantization and Quantum Field Theory written by Nima Moshayedi and published by Springer Nature. This book was released on 2022-08-11 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to deformation quantization and its relation to quantum field theory, with a focus on the constructions of Kontsevich and Cattaneo & Felder. This subject originated from an attempt to understand the mathematical structure when passing from a commutative classical algebra of observables to a non-commutative quantum algebra of observables. Developing deformation quantization as a semi-classical limit of the expectation value for a certain observable with respect to a special sigma model, the book carefully describes the relationship between the involved algebraic and field-theoretic methods. The connection to quantum field theory leads to the study of important new field theories and to insights in other parts of mathematics such as symplectic and Poisson geometry, and integrable systems. Based on lectures given by the author at the University of Zurich, the book will be of interest to graduate students in mathematics or theoretical physics. Readers will be able to begin the first chapter after a basic course in Analysis, Linear Algebra and Topology, and references are provided for more advanced prerequisites.
Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821851756
Total Pages : 434 pages
Book Rating : 4.8/5 (218 download)
Download or read book $C^*$-Algebras: 1943-1993 written by and published by American Mathematical Soc.. This book was released on 1994 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Liming Ge
Publisher : American Mathematical Soc.
ISBN 13 : 0821810936
Total Pages : 416 pages
Book Rating : 4.8/5 (218 download)
Download or read book Operator Algebras and Operator Theory written by Liming Ge and published by American Mathematical Soc.. This book was released on 1998 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings from the International Conference on Operator Algebras and Operator Theory held at the East China Normal University in Shanghai (China). Participants in the conference ranged from graduate students to postdocs to leading experts who came from around the world. Topics covered were $C*$-algebras, von Neumann algebras, non-self-adjoint operator algebras, wavelets, operator spaces and other related areas. This work consists of contributions from invited speakers and some mathematicians who were unable to attend. It presents important mathematical ideas while maintaining the uniqueness and excitement of this very successful event.
Author : Piergiulio Tempesta
Publisher : American Mathematical Soc.
ISBN 13 : 0821833294
Total Pages : 362 pages
Book Rating : 4.8/5 (218 download)
Download or read book Superintegrability in Classical and Quantum Systems written by Piergiulio Tempesta and published by American Mathematical Soc.. This book was released on 2004 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Superintegrable systems are integrable systems (classical and quantum) that have more integrals of motion than degrees of freedom. Such systems have many interesting properties. This title is based on the Workshop on Superintegrability in Classical and Quantum Systems organized by the Centre de Recherches Mathematiques in Montreal (Quebec).
Author : Reinhard Honegger
Publisher : World Scientific
ISBN 13 : 9814618853
Total Pages : 2353 pages
Book Rating : 4.8/5 (146 download)
Download or read book Photons In Fock Space And Beyond (In 3 Volumes) written by Reinhard Honegger and published by World Scientific. This book was released on 2015-04-22 with total page 2353 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three-volume major reference “Photons in Fock Space and Beyond” undertakes a new mathematical and conceptual foundation of the theory of light emphasizing mesoscopic radiation systems. The quantum optical notions are generalized beyond Fock representations where the richness of an infinite dimensional quantum field system, with its mathematical difficulties and theoretical possibilities, is fully taken into account. It aims at a microscopic formulation of a mesoscopic model class which covers in principle all stages of the generation and propagation of light within a unified and well-defined conceptual frame.The dynamics of the interacting systems is founded — according to original works of the authors — on convergent perturbation series and describes the developments of the quantized microscopic as well as the classical collective degrees of freedom at the same time. The achieved theoretical unification fits especially to laser and microwave applications inheriting objective information over quantum noise.A special advancement is the incorporation of arbitrary multiply connected cavities where ideal conductor boundary conditions are imposed. From there arises a new category of classical and quantized field parts, apparently not treated in Quantum Electrodynamics before. In combination with gauge theory, the additional “cohomological fields” explain topological quantum effects in superconductivity. Further applications are to be expected for optoelectronic and optomechanical systems.
Author : Ursula Carow-Watamura
Publisher : Springer Science & Business Media
ISBN 13 : 9783540239000
Total Pages : 316 pages
Book Rating : 4.2/5 (39 download)
Download or read book Quantum Field Theory and Noncommutative Geometry written by Ursula Carow-Watamura and published by Springer Science & Business Media. This book was released on 2005-02-21 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume reflects the growing collaboration between mathematicians and theoretical physicists to treat the foundations of quantum field theory using the mathematical tools of q-deformed algebras and noncommutative differential geometry. A particular challenge is posed by gravity, which probably necessitates extension of these methods to geometries with minimum length and therefore quantization of space. This volume builds on the lectures and talks that have been given at a recent meeting on "Quantum Field Theory and Noncommutative Geometry." A considerable effort has been invested in making the contributions accessible to a wider community of readers - so this volume will not only benefit researchers in the field but also postgraduate students and scientists from related areas wishing to become better acquainted with this field.
Author : David R Ely
Publisher : David R Ely
ISBN 13 :
Total Pages : 88 pages
Book Rating : 4./5 ( download)
Download or read book The Realm of Sedenions written by David R Ely and published by David R Ely. This book was released on 2024-05-22 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The Realm of Sedenions: A Look Into Higher-Complex Numbers" dives into the fascinating world of sedenions, a 16-dimensional number system with unique properties. The book explores the motivation behind studying sedenions, their formal definition with addition and non-commutative, non-associative multiplication, and how they differ from familiar number systems like real and complex numbers. While sedenions lack widespread practical applications yet, the book delves into potential areas of exploration in physics and computer science. It also highlights the challenges mathematicians face due to the complex multiplication rules and the lack of a straightforward geometric interpretation for these high-dimensional numbers. The book provides historical context by mentioning James Joseph Sylvester, who introduced sedenions. While directly visualizing 16 dimensions is difficult, the book discusses potential approaches like subspace projections and geometric analogies to gain a better understanding. Exercises tailored to the audience's level and a resource section for further exploration round out the book, making it a valuable resource for anyone curious about venturing beyond the realm of familiar numbers.
Author : Sylvie Paycha
Publisher : American Mathematical Soc.
ISBN 13 : 0821840622
Total Pages : 272 pages
Book Rating : 4.8/5 (218 download)
Download or read book Geometric and Topological Methods for Quantum Field Theory written by Sylvie Paycha and published by American Mathematical Soc.. This book was released on 2007 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Víctor Aldaya
Publisher : Universidad de Salamanca
ISBN 13 : 9788478006397
Total Pages : 552 pages
Book Rating : 4.0/5 (63 download)
Download or read book Symmetries in gravity and field theory written by Víctor Aldaya and published by Universidad de Salamanca. This book was released on 2004-01-01 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Pavel Exner
Publisher : World Scientific
ISBN 13 : 9814304638
Total Pages : 709 pages
Book Rating : 4.8/5 (143 download)
Download or read book XVIth International Congress on Mathematical Physics written by Pavel Exner and published by World Scientific. This book was released on 2010 with total page 709 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Congress on Mathematical Physics is the flagship conference in this exciting field. Convening every three years, it gives a survey on the progress achieved in all branches of mathematical physics. It also provides a superb platform to discuss challenges and new ideas. The present volume collects material from the XVIth ICMP which was held in Prague, August 2009, and features most of the plenary lectures and invited lectures in topical sessions as well as information on other parts of the congress program. This volume provides a broad coverage of the field of mathematical physics, from dominantly mathematical subjects to particle physics, condensed matter, and application of mathematical physics methods in various areas such as astrophysics and ecology, amongst others.
Author : Klaas Landsman
Publisher : Springer
ISBN 13 : 3319517775
Total Pages : 881 pages
Book Rating : 4.3/5 (195 download)
Download or read book Foundations of Quantum Theory written by Klaas Landsman and published by Springer. This book was released on 2017-05-11 with total page 881 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory. This book is Open Access under a CC BY licence.
Author : P. Tempesta, P. Winternitz, J. Harnad, W. Miller, Jr., G. Pogosyan, and M. Rodriguez
Publisher : American Mathematical Soc.
ISBN 13 : 9780821870327
Total Pages : 364 pages
Book Rating : 4.8/5 (73 download)
Download or read book Superintegrability in Classical and Quantum Systems written by P. Tempesta, P. Winternitz, J. Harnad, W. Miller, Jr., G. Pogosyan, and M. Rodriguez and published by American Mathematical Soc.. This book was released on with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Superintegrable systems are integrable systems (classical and quantum) that have more integrals of motion than degrees of freedom. Such systems have many interesting properties. This title is based on the Workshop on Superintegrability in Classical and Quantum Systems organized by the Centre de Recherches Mathematiques in Montreal (Quebec).
Author : Andrei Y. Khrennikov
Publisher : Springer Science & Business Media
ISBN 13 : 1402095937
Total Pages : 354 pages
Book Rating : 4.4/5 (2 download)
Download or read book Contextual Approach to Quantum Formalism written by Andrei Y. Khrennikov and published by Springer Science & Business Media. This book was released on 2009-05-21 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to show that the probabilistic formalisms of classical statistical mechanics and quantum mechanics can be unified on the basis of a general contextual probabilistic model. By taking into account the dependence of (classical) probabilities on contexts (i.e. complexes of physical conditions), one can reproduce all distinct features of quantum probabilities such as the interference of probabilities and the violation of Bell’s inequality. Moreover, by starting with a formula for the interference of probabilities (which generalizes the well known classical formula of total probability), one can construct the representation of contextual probabilities by complex probability amplitudes or, in the abstract formalism, by normalized vectors of the complex Hilbert space or its hyperbolic generalization. Thus the Hilbert space representation of probabilities can be naturally derived from classical probabilistic assumptions. An important chapter of the book critically reviews known no-go theorems: the impossibility to establish a finer description of micro-phenomena than provided by quantum mechanics; and, in particular, the commonly accepted consequences of Bell’s theorem (including quantum non-locality). Also, possible applications of the contextual probabilistic model and its quantum-like representation in complex Hilbert spaces in other fields (e.g. in cognitive science and psychology) are discussed.
