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Author :
Publisher :
ISBN 13 :
Total Pages : 49 pages
Book Rating : 4.:/5 (933 download)
Download or read book Géométrie non commutative et physique quantique written by and published by . This book was released on 1992* with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Alain Connes
Publisher : Companyédition CNRS/De Vive Voix
ISBN 13 : 9782271127129
Total Pages : 73 pages
Book Rating : 4.1/5 (271 download)
Download or read book La géométrie et le quantique written by Alain Connes and published by Companyédition CNRS/De Vive Voix. This book was released on 2019-09-26 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt: La 4e de couverture indique : "En 1637, Descartes révolutionne la manière que l'on a de faire de la géométrie : en associant à chaque point de l'espace trois coordonnéees, il pose les bases de la géométrie algébrique. Cette géométrie est dite "commutative" : le produit de deux quantités ne dépend pas de l'ordre des termes, et A x B = B x A. Cette propriété est fondamentale, l'ensemble de l'édifice mathématique en dépend. Mais au début du XXe siècle, la découverte du monde quantique vient tout bouleverser. L'espace géométrique des états d'un système microscopique, un atome par exemple,s'enrichit de nouvelles propriétés, qui ne commutent plus. Il faut donc adapter l'ensemble des outils mathématiques. Cette nouvelle géométrie, dite "non commutative", devenue essentielle à la recherche en physique, a été développé par Alain Connes. En un texte court, vif et fascinant, ce grand mathématicien nous introduit à la poésie de sa discipline."
Author : Olav Arnfinn Laudal
Publisher : World Scientific
ISBN 13 : 981434334X
Total Pages : 154 pages
Book Rating : 4.8/5 (143 download)
Download or read book Geometry of Time-spaces written by Olav Arnfinn Laudal and published by World Scientific. This book was released on 2011 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a monograph about non-commutative algebraic geometry, and its application to physics. The main mathematical inputs are the non-commutative deformation theory, moduli theory of representations of associative algebras, a new non-commutative theory of phase spaces, and its canonical Dirac derivation. The book starts with a new definition of time, relative to which the set of mathematical velocities form a compact set, implying special and general relativity. With this model in mind, a general Quantum Theory is developed and shown to fit with the classical theory. In particular the ?toy?-model used as example, contains, as part of the structure, the classical gauge groups u(1), su(2) and su(3), and therefore also the theory of spin and quarks, etc.
Author : Robert Coquereaux
Publisher : World Scientific
ISBN 13 : 9814549320
Total Pages : 414 pages
Book Rating : 4.8/5 (145 download)
Download or read book Infinite Dimensional Geometry, Noncommutative Geometry, Operator Algebras And Fundamental Interactions - Proceedings Of The First Caribbean Spring School Of Mathematics And Theoretical Physics written by Robert Coquereaux and published by World Scientific. This book was released on 1995-06-28 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Huzihiro Araki
Publisher : Springer Science & Business Media
ISBN 13 : 9401728232
Total Pages : 452 pages
Book Rating : 4.4/5 (17 download)
Download or read book Quantum and Non-Commutative Analysis written by Huzihiro Araki and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the past decade, there has been a sudden and vigorous development in a number of research areas in mathematics and mathematical physics, such as theory of operator algebras, knot theory, theory of manifolds, infinite dimensional Lie algebras and quantum groups (as a new topics), etc. on the side of mathematics, quantum field theory and statistical mechanics on the side of mathematical physics. The new development is characterized by very strong relations and interactions between different research areas which were hitherto considered as remotely related. Focussing on these new developments in mathematical physics and theory of operator algebras, the International Oji Seminar on Quantum Analysis was held at the Kansai Seminar House, Kyoto, JAPAN during June 25-29, 1992 by a generous sponsorship of the Japan Society for the Promotion of Science and the Fujihara Foundation of Science, as a workshop of relatively small number of (about 50) invited participants. This was followed by an open Symposium at RIMS, described below by its organizer, A. Kishimoto. The Oji Seminar began with two key-note addresses, one by V.F.R. Jones on Spin Models in Knot Theory and von Neumann Algebras and by A. Jaffe on Where Quantum Field Theory Has Led. Subsequently topics such as Subfactors and Sector Theory, Solvable Models of Statistical Mechanics, Quantum Field Theory, Quantum Groups, and Renormalization Group Ap proach, are discussed. Towards the end, a panel discussion on Where Should Quantum Analysis Go? was held.
Author : Franco Strocchi
Publisher : World Scientific Publishing Company
ISBN 13 : 981310659X
Total Pages : 157 pages
Book Rating : 4.8/5 (131 download)
Download or read book Introduction To The Mathematical Structure Of Quantum Mechanics, An: A Short Course For Mathematicians written by Franco Strocchi and published by World Scientific Publishing Company. This book was released on 2005-11-17 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book arises out of the need for Quantum Mechanics (QM) to be part of the common education of mathematics students. Rather than starting from the Dirac-Von Neumann axioms, the book offers a short presentation of the mathematical structure of QM using the C--algebraic structure of the observable based on the operational definition of measurements and the duality between states and observables. The description of states and observables as Hilbert space vectors and operators is then derived from the GNS and Gelfand-Naimark Theorems.For finite degrees of freedom, the Weyl algebra codifies the experimental limitations on the measurements of position and momentum (Heisenberg uncertainty relations) and Schroedinger QM follows from the von Neumann uniqueness theorem.The existence problem of the dynamics is related to the self-adjointness of the differential operator describing the Hamiltonian and solved by the Rellich-Kato theorems. Examples are discussed which include the explanation of the discreteness of the atomic spectra.Because of the increasing interest in the relation between QM and stochastic processes, a final chapter is devoted to the functional integral approach (Feynman-Kac formula), the formulation in terms of ground state correlations (Wightman functions) and their analytic continuation to imaginary time (Euclidean QM). The quantum particle on a circle as an example of the interplay between topology and functional integral is also discussed in detail.
Author : Jose M. Gracia-Bondia
Publisher : Springer Science & Business Media
ISBN 13 : 1461200059
Total Pages : 692 pages
Book Rating : 4.4/5 (612 download)
Download or read book Elements of Noncommutative Geometry written by Jose M. Gracia-Bondia and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Giovanni Landi
Publisher : Springer Science & Business Media
ISBN 13 : 354014949X
Total Pages : 216 pages
Book Rating : 4.5/5 (41 download)
Download or read book An Introduction to Noncommutative Spaces and Their Geometries written by Giovanni Landi and published by Springer Science & Business Media. This book was released on 2003-07-01 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes are an introduction to several ideas and applications of noncommutative geometry. It starts with a not necessarily commutative but associative algebra which is thought of as the algebra of functions on some 'virtual noncommutative space'. Attention is switched from spaces, which in general do not even exist, to algebras of functions. In these notes, particular emphasis is put on seeing noncommutative spaces as concrete spaces, namely as a collection of points with a topology. The necessary mathematical tools are presented in a systematic and accessible way and include among other things, C'*-algebras, module theory and K-theory, spectral calculus, forms and connection theory. Application to Yang--Mills, fermionic, and gravity models are described. Also the spectral action and the related invariance under automorphism of the algebra is illustrated. Some recent work on noncommutative lattices is presented. These lattices arose as topologically nontrivial approximations to 'contuinuum' topological spaces. They have been used to construct quantum-mechanical and field-theory models, alternative models to lattice gauge theory, with nontrivial topological content. This book will be essential to physicists and mathematicians with an interest in noncommutative geometry and its uses in physics.
Author : Ludwig Pittner
Publisher : Springer Science & Business Media
ISBN 13 : 3540478019
Total Pages : 476 pages
Book Rating : 4.5/5 (44 download)
Download or read book Algebraic Foundations of Non-Commutative Differential Geometry and Quantum Groups written by Ludwig Pittner and published by Springer Science & Business Media. This book was released on 2009-01-29 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum groups and quantum algebras as well as non-commutative differential geometry are important in mathematics and considered to be useful tools for model building in statistical and quantum physics. This book, addressing scientists and postgraduates, contains a detailed and rather complete presentation of the algebraic framework. Introductory chapters deal with background material such as Lie and Hopf superalgebras, Lie super-bialgebras, or formal power series. Great care was taken to present a reliable collection of formulae and to unify the notation, making this volume a useful work of reference for mathematicians and mathematical physicists.
Author : Franco Strocchi
Publisher : World Scientific Publishing Company
ISBN 13 : 9813107367
Total Pages : 193 pages
Book Rating : 4.8/5 (131 download)
Download or read book Introduction To The Mathematical Structure Of Quantum Mechanics, An: A Short Course For Mathematicians (2nd Edition) written by Franco Strocchi and published by World Scientific Publishing Company. This book was released on 2008-10-30 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second printing contains a critical discussion of Dirac derivation of canonical quantization, which is instead deduced from general geometric structures. This book arises out of the need for Quantum Mechanics (QM) to be part of the common education of mathematics students. The mathematical structure of QM is formulated in terms of the C*-algebra of observables, which is argued on the basis of the operational definition of measurements and the duality between states and observables, for a general physical system.The Dirac-von Neumann axioms are then derived. The description of states and observables as Hilbert space vectors and operators follows from the GNS and Gelfand-Naimark Theorems. The experimental existence of complementary observables for atomic systems is shown to imply the noncommutativity of the observable algebra, the distinctive feature of QM; for finite degrees of freedom, the Weyl algebra codifies the experimental complementarity of position and momentum (Heisenberg commutation relations) and Schrödinger QM follows from the von Neumann uniqueness theorem.The existence problem of the dynamics is related to the self-adjointness of the Hamiltonian and solved by the Kato-Rellich conditions on the potential, which also guarantee quantum stability for classically unbounded-below Hamiltonians. Examples are discussed which include the explanation of the discreteness of the atomic spectra.Because of the increasing interest in the relation between QM and stochastic processes, a final chapter is devoted to the functional integral approach (Feynman-Kac formula), to the formulation in terms of ground state correlations (the quantum mechanical analog of the Wightman functions) and their analytic continuation to imaginary time (Euclidean QM). The quantum particle on a circle is discussed in detail, as an example of the interplay between topology and functional integral, leading to the emergence of superselection rules and θ sectors.
Author : Steven Duplij
Publisher : Springer Science & Business Media
ISBN 13 : 9780792369998
Total Pages : 498 pages
Book Rating : 4.3/5 (699 download)
Download or read book Noncommutative Structures in Mathematics and Physics written by Steven Duplij and published by Springer Science & Business Media. This book was released on 2001-05-31 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: A presentation of outstanding achievements and ideas, of both eastern and western scientists, both mathematicians and physicists. Their presentations of recent work on quantum field theory, supergravity, M-theory, black holes and quantum gravity, together with research into noncommutative geometry, Hopf algebras, representation theory, categories and quantum groups, take the reader to the forefront of the latest developments. Other topics covered include supergravity and branes, supersymmetric quantum mechanics and superparticles, (super) black holes, superalgebra representations, and SUSY GUT phenomenology. Essential reading for workers in the modern methods of theoretical and mathematical physics.
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 : Gerhard Grensing
Publisher : World Scientific
ISBN 13 : 9811237093
Total Pages : 1656 pages
Book Rating : 4.8/5 (112 download)
Download or read book Structural Aspects Of Quantum Field Theory And Noncommutative Geometry (Second Edition) (In 2 Volumes) written by Gerhard Grensing and published by World Scientific. This book was released on 2021-07-15 with total page 1656 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the subject of quantum field theory. It is divided into two volumes. The first volume can serve as a textbook on main techniques and results of quantum field theory, while the second treats more recent developments, in particular the subject of quantum groups and noncommutative geometry, and their interrelation.The second edition is extended by additional material, mostly concerning the impact of noncommutative geometry on theories beyond the standard model of particle physics, especially the possible role of torsion in the context of the dark matter problem. Furthermore, the text includes a discussion of the Randall-Sundrum model and the Seiberg-Witten equations.
Author : Yoshiaki Maeda
Publisher : World Scientific
ISBN 13 : 9813144629
Total Pages : 413 pages
Book Rating : 4.8/5 (131 download)
Download or read book Noncommutative Geometry And Physics 4 - Workshop On Strings, Membranes And Topological Field Theory written by Yoshiaki Maeda and published by World Scientific. This book was released on 2017-03-16 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of the lectures and talks presented in the Tohoku Forum for Creativity in the thematic year 2015 'Fundamental Problems in Quantum Physics: Strings, Black Holes and Quantum Information', and related events in the period 2014-2016.This volume especially contains an overview of recent developments in the theory of strings and membranes, as well as topological field theory.
Author : Florian Girelli
Publisher :
ISBN 13 :
Total Pages : 181 pages
Book Rating : 4.:/5 (492 download)
Download or read book Géométrie non commutative et gravité quantique written by Florian Girelli and published by . This book was released on 2002 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: La géométrie non commutative permet d'incorporer des notions quantiques en géométrie. Elle semble donc l'outil idéal pour étudier le problème de la quantification de la relativité générale. Cette thèse a pour but d'introduire les notions de géométrie non commutative, de gravité quantique (approche des Mousses de Spin) et de donner des directions possibles sur l'utilisation des structures de la GNC afin d'étudier la gravité quantique (non perturbative). La première partie présente une introduction rapide à la GNC et à son application au modèle standard, par le biais des géométries presque commutatives. Le fait que ces dernières permettent de mettre au même plan gravité et Yang-Mills-Higgs est rappelé. Pour illustrer cette construction, les modèles droite gauche symétriques sont étudiés, et je montre qu'ils ne peuvent pas être viables physiquement. La deuxième partie traite de la théorie des champs et de la renormalisation vue par le biais d'algèbre de Hopf de structures graphiques : arbres avec racine ou diagrammes de Feynman. La construction de Connes et Kreimer, dans le cadre de la régularisation dimensionnelle, est ensuite rappelée et je montre comment elle s'étend pour tenir compte de la renormalisation de la fonction d'onde. Je considère ensuite le cas de la renormalisation à la Polchinski et je montre comment les algèbres de Hopf des arbres et des diagrammes interviennent, ce qui permet à la fois de simplifier la preuve de la renormalisabilité mais aussi de définir une application entre arbres avec racine et diagrammes de Feynman. Je donne finalement des arguments en vue d'une application de ces structures au cadre des Mousses de Spin, ou la construction perturbative d'observables pour la relativité générale. La troisième partie introduit la construction des Mousses de Spin en 3d. Je montre d'abord comment la quantification de la gravité en 3d s'effectue en utilisant les représentations du groupe considéré. Je montre ensuite comment en introduisant une diagrammatique, on peut simplifier la preuve de l'invariance topologique de la fonction de partition et même définir le modèle sur des décompositions cellulaires quelconques. Je donne finalement quelques arguments sur une utilisation directe de la GNC dans le cadre des Mousses de Spin, en utilisant les posets.
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 : Alain Connes
Publisher : Springer
ISBN 13 : 3540397027
Total Pages : 364 pages
Book Rating : 4.5/5 (43 download)
Download or read book Noncommutative Geometry written by Alain Connes and published by Springer. This book was released on 2003-12-15 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.
