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Noncommutative Differential Geometry And Its Applications To Physics
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Book Synopsis Noncommutative Differential Geometry and Its Applications to Physics by : Yoshiaki Maeda
Download or read book Noncommutative Differential Geometry and Its Applications to Physics written by Yoshiaki Maeda and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative differential geometry is a new approach to classical geometry. It was originally used by Fields Medalist A. Connes in the theory of foliations, where it led to striking extensions of Atiyah-Singer index theory. It also may be applicable to hitherto unsolved geometric phenomena and physical experiments. However, noncommutative differential geometry was not well understood even among mathematicians. Therefore, an international symposium on commutative differential geometry and its applications to physics was held in Japan, in July 1999. Topics covered included: deformation problems, Poisson groupoids, operad theory, quantization problems, and D-branes. The meeting was attended by both mathematicians and physicists, which resulted in interesting discussions. This volume contains the refereed proceedings of this symposium. Providing a state of the art overview of research in these topics, this book is suitable as a source book for a seminar in noncommutative geometry and physics.
Book Synopsis An Introduction to Noncommutative Differential Geometry and Its Physical Applications by : J. Madore
Download or read book An Introduction to Noncommutative Differential Geometry and Its Physical Applications written by J. Madore and published by Cambridge University Press. This book was released on 1999-06-24 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thoroughly revised introduction to non-commutative geometry.
Book Synopsis Noncommutative Geometry and Physics 3 by : Giuseppe Dito
Download or read book Noncommutative Geometry and Physics 3 written by Giuseppe Dito and published by World Scientific. This book was released on 2013-01-11 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative differential geometry is a novel approach to geometry, aimed in part at applications in physics. It was founded in the early eighties by the 1982 Fields Medalist Alain Connes on the basis of his fundamental works in operator algebras. It is now a very active branch of mathematics with actual and potential applications to a variety of domains in physics ranging from solid state to quantization of gravity. The strategy is to formulate usual differential geometry in a somewhat unusual manner, using in particular operator algebras and related concepts, so as to be able to plug in noncommutativity in a natural way. Algebraic tools such as K-theory and cyclic cohomology and homology play an important role in this field. It is an important topic both for mathematics and physics. Contents:K-Theory and D-Branes, Shonan:The Local Index Formula in Noncommutative Geometry Revisited (Alan L Carey, John Phillips, Adam Rennie and Fedor A Sukochev)Semi-Finite Noncommutative Geometry and Some Applications (Alan L Carey, John Phillips and Adam Rennie)Generalized Geometries in String Compactification Scenarios (Tetsuji Kimura)What Happen to Gauge Theories under Noncommutative Deformation? (Akifumi Sako)D-Branes and Bivariant K-Theory (Richard J Szabo)Two-Sided Bar Constructions for Partial Monoids and Applications to K-Homology Theory (Dai Tamaki)Twisting Segal's K-Homology Theory (Dai Tamaki)Spectrum of Non-Commutative Harmonic Oscillators and Residual Modular Forms (Kazufumi Kimoto and Masato Wakayama)Coarse Embeddings and Higher Index Problems for Expanders (Qin Wang)Deformation Quantization and Noncommutative Geometry, RIMS:Enriched Fell Bundles and Spaceoids (Paolo Bertozzini, Roberto Conti and Wicharn Lewkeeratiyutkul)Weyl Character Formula in KK-Theory (Jonathan Block and Nigel Higson)Recent Advances in the Study of the Equivariant Brauer Group (Peter Bouwknegt, Alan Carey and Rishni Ratnam)Entire Cyclic Cohomology of Noncommutative Manifolds (Katsutoshi Kawashima)Geometry of Quantum Projective Spaces (Francesco D'Andrea and Giovanni Landi)On Yang–Mills Theory for Quantum Heisenberg Manifolds (Hyun Ho Lee)Dilatational Equivalence Classes and Novikov–Shubin Type Capacities of Groups, and Random Walks (Shin-ichi Oguni)Deformation Quantization of Gauge Theory in ℝ4 and U(1) Instanton Problems (Yoshiaki Maeda and Akifumi Sako)Dualities in Field Theories and the Role of K-Theory (Jonathan Rosenberg)Dualities in Field Theories and the Role of K-Theory (Jonathan Rosenberg) Readership: Researchers and graduate students in Mathematical Physics and Applied Mathematics. Keywords:Noncommutative Geometry;Deformation Quantizations;D-Brane;K-Theory;T-Duality
Book Synopsis Noncommutative Geometry and Particle Physics by : Walter D. van Suijlekom
Download or read book Noncommutative Geometry and Particle Physics written by Walter D. van Suijlekom and published by Springer. This book was released on 2014-07-21 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to noncommutative geometry and presents a number of its recent applications to particle physics. It is intended for graduate students in mathematics/theoretical physics who are new to the field of noncommutative geometry, as well as for researchers in mathematics/theoretical physics with an interest in the physical applications of noncommutative geometry. In the first part, we introduce the main concepts and techniques by studying finite noncommutative spaces, providing a “light” approach to noncommutative geometry. We then proceed with the general framework by defining and analyzing noncommutative spin manifolds and deriving some main results on them, such as the local index formula. In the second part, we show how noncommutative spin manifolds naturally give rise to gauge theories, applying this principle to specific examples. We subsequently geometrically derive abelian and non-abelian Yang-Mills gauge theories, and eventually the full Standard Model of particle physics, and conclude by explaining how noncommutative geometry might indicate how to proceed beyond the Standard Model.
Book Synopsis An Introduction to Noncommutative Geometry by : Joseph C. Várilly
Download or read book An Introduction to Noncommutative Geometry written by Joseph C. Várilly and published by European Mathematical Society. This book was released on 2006 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative geometry, inspired by quantum physics, describes singular spaces by their noncommutative coordinate algebras and metric structures by Dirac-like operators. Such metric geometries are described mathematically by Connes' theory of spectral triples. These lectures, delivered at an EMS Summer School on noncommutative geometry and its applications, provide an overview of spectral triples based on examples. This introduction is aimed at graduate students of both mathematics and theoretical physics. It deals with Dirac operators on spin manifolds, noncommutative tori, Moyal quantization and tangent groupoids, action functionals, and isospectral deformations. The structural framework is the concept of a noncommutative spin geometry; the conditions on spectral triples which determine this concept are developed in detail. The emphasis throughout is on gaining understanding by computing the details of specific examples. The book provides a middle ground between a comprehensive text and a narrowly focused research monograph. It is intended for self-study, enabling the reader to gain access to the essentials of noncommutative geometry. New features since the original course are an expanded bibliography and a survey of more recent examples and applications of spectral triples.
Book Synopsis Noncommutative Geometry and the Standard Model of Elementary Particle Physics by : Florian Scheck
Download or read book Noncommutative Geometry and the Standard Model of Elementary Particle Physics written by Florian Scheck and published by Springer Science & Business Media. This book was released on 2002-11-26 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The outcome of a close collaboration between mathematicians and mathematical physicists, these Lecture Notes present the foundations of A. Connes noncommutative geometry, as well as its applications in particular to the field of theoretical particle physics. The coherent and systematic approach makes this book useful for experienced researchers and postgraduate students alike.
Book Synopsis Noncommutative Geometry by : Alain Connes
Download or read book Noncommutative Geometry written by Alain Connes and published by Springer Science & Business Media. This book was released on 2003-12-08 with total page 372 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.
Book Synopsis Noncommutative Geometry by : Alain Connes
Download or read book Noncommutative Geometry written by Alain Connes and published by Academic Press. This book was released on 1995-01-17 with total page 678 pages. Available in PDF, EPUB and Kindle. Book excerpt: This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields. First full treatment of the subject and its applications Written by the pioneer of this field Broad applications in mathematics Of interest across most fields Ideal as an introduction and survey Examples treated include: the space of Penrose tilings the space of leaves of a foliation the space of irreducible unitary representations of a discrete group the phase space in quantum mechanics the Brillouin zone in the quantum Hall effect A model of space time
Book Synopsis Analysis And Mathematical Physics by : Bullett Shaun
Download or read book Analysis And Mathematical Physics written by Bullett Shaun and published by World Scientific. This book was released on 2016-12-22 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a concise reference book on analysis and mathematical physics, leading readers from a foundation to advanced level understanding of the topic. This is the perfect text for graduate or PhD mathematical-science students looking for support in topics such as distributions, Fourier transforms and microlocal analysis, C* Algebras, value distribution of meromorphic functions, noncommutative differential geometry, differential geometry and mathematical physics, mathematical problems of general relativity, and special functions of mathematical physics. Analysis and Mathematical Physics is the sixth volume of the LTCC Advanced Mathematics Series. This series is the first to provide advanced introductions to mathematical science topics to advanced students of mathematics. Editor the three joint heads of the London Taught Course Centre for PhD Students in the Mathematical Sciences (LTCC), each book supports readers in broadening their mathematical knowledge outside of their immediate research disciplines while also covering specialized key areas.
Book Synopsis Differential Geometry and Mathematical Physics by : John K. Beem
Download or read book Differential Geometry and Mathematical Physics written by John K. Beem and published by American Mathematical Soc.. This book was released on 1994 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the Special Session, Geometric Methods in Mathematical Physics, held at the joint AMS-CMS meeting in Vancouver in August 1993. The papers collected here contain a number of new results in differential geometry and its applications to physics. The major themes include black holes, singularities, censorship, the Einstein field equations, geodesics, index theory, submanifolds, CR-structures, and space-time symmetries. In addition, there are papers on Yang-Mills fields, geometric techniques in control theory, and equilibria. Containing new results by established researchers in the field, this book provides a look at developments in this exciting area of research.
Author :Jose M. Gracia-Bondia Publisher :Springer Science & Business Media ISBN 13 :1461200059 Total Pages :692 pages Book Rating :4.4/5 (612 download)
Book Synopsis Elements of Noncommutative Geometry by : Jose M. Gracia-Bondia
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:
Book Synopsis Differential Geometry for Physicists by : Bo-Yu Hou
Download or read book Differential Geometry for Physicists written by Bo-Yu Hou and published by World Scientific Publishing Company. This book was released on 1997-10-31 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is divided into fourteen chapters, with 18 appendices as introduction to prerequisite topological and algebraic knowledge, etc. The first seven chapters focus on local analysis. This part can be used as a fundamental textbook for graduate students of theoretical physics. Chapters 8–10 discuss geometry on fibre bundles, which facilitates further reference for researchers. The last four chapters deal with the Atiyah-Singer index theorem, its generalization and its application, quantum anomaly, cohomology field theory and noncommutative geometry, giving the reader a glimpse of the frontier of current research in theoretical physics.
Book Synopsis Noncommutative Geometry and Particle Physics by : Walter van Suijlekom
Download or read book Noncommutative Geometry and Particle Physics written by Walter van Suijlekom and published by Springer. This book was released on 2014-07-27 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to noncommutative geometry and presents a number of its recent applications to particle physics. It is intended for graduate students in mathematics/theoretical physics who are new to the field of noncommutative geometry, as well as for researchers in mathematics/theoretical physics with an interest in the physical applications of noncommutative geometry. In the first part, we introduce the main concepts and techniques by studying finite noncommutative spaces, providing a “light” approach to noncommutative geometry. We then proceed with the general framework by defining and analyzing noncommutative spin manifolds and deriving some main results on them, such as the local index formula. In the second part, we show how noncommutative spin manifolds naturally give rise to gauge theories, applying this principle to specific examples. We subsequently geometrically derive abelian and non-abelian Yang-Mills gauge theories, and eventually the full Standard Model of particle physics, and conclude by explaining how noncommutative geometry might indicate how to proceed beyond the Standard Model.
Book Synopsis Noncommutative Geometry, Quantum Fields and Motives by : Alain Connes
Download or read book Noncommutative Geometry, Quantum Fields and Motives written by Alain Connes and published by American Mathematical Soc.. This book was released on 2019-03-13 with total page 785 pages. Available in PDF, EPUB and Kindle. Book excerpt: The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book deals with quantum field theory and the geometric structure of renormalization as a Riemann-Hilbert correspondence. It also presents a model of elementary particle physics based on noncommutative geometry. The main result is a complete derivation of the full Standard Model Lagrangian from a very simple mathematical input. Other topics covered in the first part of the book are a noncommutative geometry model of dimensional regularization and its role in anomaly computations, and a brief introduction to motives and their conjectural relation to quantum field theory. The second part of the book gives an interpretation of the Weil explicit formula as a trace formula and a spectral realization of the zeros of the Riemann zeta function. This is based on the noncommutative geometry of the adèle class space, which is also described as the space of commensurability classes of Q-lattices, and is dual to a noncommutative motive (endomotive) whose cyclic homology provides a general setting for spectral realizations of zeros of L-functions. The quantum statistical mechanics of the space of Q-lattices, in one and two dimensions, exhibits spontaneous symmetry breaking. In the low-temperature regime, the equilibrium states of the corresponding systems are related to points of classical moduli spaces and the symmetries to the class field theory of the field of rational numbers and of imaginary quadratic fields, as well as to the automorphisms of the field of modular functions. The book ends with a set of analogies between the noncommutative geometries underlying the mathematical formulation of the Standard Model minimally coupled to gravity and the moduli spaces of Q-lattices used in the study of the zeta function.
Book Synopsis Advances in Noncommutative Geometry by : Ali Chamseddine
Download or read book Advances in Noncommutative Geometry written by Ali Chamseddine and published by Springer Nature. This book was released on 2020-01-13 with total page 753 pages. Available in PDF, EPUB and Kindle. Book excerpt: This authoritative volume in honor of Alain Connes, the foremost architect of Noncommutative Geometry, presents the state-of-the art in the subject. The book features an amalgam of invited survey and research papers that will no doubt be accessed, read, and referred to, for several decades to come. The pertinence and potency of new concepts and methods are concretely illustrated in each contribution. Much of the content is a direct outgrowth of the Noncommutative Geometry conference, held March 23–April 7, 2017, in Shanghai, China. The conference covered the latest research and future areas of potential exploration surrounding topology and physics, number theory, as well as index theory and its ramifications in geometry.
Book Synopsis Methods of Noncommutative Geometry for Group C*-Algebras by : Do Ngoc Diep
Download or read book Methods of Noncommutative Geometry for Group C*-Algebras written by Do Ngoc Diep and published by CRC Press. This book was released on 1999-12-06 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description of the structure of group C*-algebras is a difficult problem, but relevant to important new developments in mathematics, such as non-commutative geometry and quantum groups. Although a significant number of new methods and results have been obtained, until now they have not been available in book form. This volume provides an introduction to and presents research on the study of group C*-algebras, suitable for all levels of readers - from graduate students to professional researchers. The introduction provides the essential features of the methods used. In Part I, the author offers an elementary overview - using concrete examples-of using K-homology, BFD functors, and KK-functors to describe group C*-algebras. In Part II, he uses advanced ideas and methods from representation theory, differential geometry, and KK-theory, to explain two primary tools used to study group C*-algebras: multidimensional quantization and construction of the index of group C*-algebras through orbit methods. The structure of group C*-algebras is an important issue both from a theoretical viewpoint and in its applications in physics and mathematics. Armed with the background, tools, and research provided in Methods of Noncommutative Geometry for Group C*-Algebras, readers can continue this work and make significant contributions to perfecting the theory and solving this problem.
Book Synopsis Basic Noncommutative Geometry by : Masoud Khalkhali
Download or read book Basic Noncommutative Geometry written by Masoud Khalkhali and published by European Mathematical Society. This book was released on 2009 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Basic Noncommutative Geometry provides an introduction to noncommutative geometry and some of its applications. The book can be used either as a textbook for a graduate course on the subject or for self-study. It will be useful for graduate students and researchers in mathematics and theoretical physics and all those who are interested in gaining an understanding of the subject. One feature of this book is the wealth of examples and exercises that help the reader to navigate through the subject. While background material is provided in the text and in several appendices, some familiarity with basic notions of functional analysis, algebraic topology, differential geometry and homological algebra at a first year graduate level is helpful. Developed by Alain Connes since the late 1970s, noncommutative geometry has found many applications to long-standing conjectures in topology and geometry and has recently made headways in theoretical physics and number theory. The book starts with a detailed description of some of the most pertinent algebra-geometry correspondences by casting geometric notions in algebraic terms, then proceeds in the second chapter to the idea of a noncommutative space and how it is constructed. The last two chapters deal with homological tools: cyclic cohomology and Connes-Chern characters in K-theory and K-homology, culminating in one commutative diagram expressing the equality of topological and analytic index in a noncommutative setting. Applications to integrality of noncommutative topological invariants are given as well."--Publisher's description.
