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Author : John P. Harnad,S. Shnider
Publisher : Berlin : Springer-Verlag
Page : 180 pages
File Size : 47,9 Mb
Release : 1980
Category : Mathematics
ISBN : UOM:39015013055549
Author : J. P. Harnad,S. Shnider
Publisher : Unknown
Page : 172 pages
File Size : 52,9 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662176572
Author : Hernan Ocampo,Eddy Pariguan,Sylvie Paycha
Publisher : Cambridge University Press
Page : 435 pages
File Size : 44,9 Mb
Release : 2010-04-29
Category : Science
ISBN : 9781139486736
Aimed at graduate students in physics and mathematics, this book provides an introduction to recent developments in several active topics at the interface between algebra, geometry, topology and quantum field theory. The first part of the book begins with an account of important results in geometric topology. It investigates the differential equation aspects of quantum cohomology, before moving on to noncommutative geometry. This is followed by a further exploration of quantum field theory and gauge theory, describing AdS/CFT correspondence, and the functional renormalization group approach to quantum gravity. The second part covers a wide spectrum of topics on the borderline of mathematics and physics, ranging from orbifolds to quantum indistinguishability and involving a manifold of mathematical tools borrowed from geometry, algebra and analysis. Each chapter presents introductory material before moving on to more advanced results. The chapters are self-contained and can be read independently of the rest.
Author : Gregory Naber
Publisher : Springer Science & Business Media
Page : 428 pages
File Size : 43,9 Mb
Release : 1997-04-24
Category : Mathematics
ISBN : 0387949461
Like any books on a subject as vast as this, this book has to have a point-of-view to guide the selection of topics. Naber takes the view that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The book weaves together rudimentary notions from the classical gauge theory of physics with the topological and geometrical concepts that became the mathematical models of these notions. The reader is asked to join the author on some vague notion of what an electromagnetic field might be, to be willing to accept a few of the more elementary pronouncements of quantum mechanics, and to have a solid background in real analysis and linear algebra and some of the vocabulary of modern algebra. In return, the book offers an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2) connections on S4 with instanton number -1.
Author : Gregory L. Naber
Publisher : Springer Science & Business Media
Page : 453 pages
File Size : 41,8 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475768503
A study of topology and geometry, beginning with a comprehensible account of the extraordinary and rather mysterious impact of mathematical physics, and especially gauge theory, on the study of the geometry and topology of manifolds. The focus of the book is the Yang-Mills-Higgs field and some considerable effort is expended to make clear its origin and significance in physics. Much of the mathematics developed here to study these fields is standard, but the treatment always keeps one eye on the physics and sacrifices generality in favor of clarity. The author brings readers up the level of physics and mathematics needed to conclude with a brief discussion of the Seiberg-Witten invariants. A large number of exercises are included to encourage active participation on the part of the reader.
Author : Anastasios Mallios
Publisher : Springer Science & Business Media
Page : 303 pages
File Size : 46,9 Mb
Release : 2006-07-27
Category : Mathematics
ISBN : 9780817644741
This is original, well-written work of interest Presents for the first time (physical) field theories written in sheaf-theoretic language Contains a wealth of minutely detailed, rigorous computations, ususally absent from standard physical treatments Author's mastery of the subject and the rigorous treatment of this text make it invaluable
Author : Gregory Naber
Publisher : Unknown
Page : 416 pages
File Size : 53,5 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 1475727437
Author : Alexander Cardona,Carolina Neira-Jiménez,Hernán Ocampo,Sylvie Paycha,Andrés F Reyes-Lega
Publisher : World Scientific
Page : 380 pages
File Size : 55,8 Mb
Release : 2013-11-15
Category : Mathematics
ISBN : 9789814460064
Based on lectures held at the 7th Villa de Leyva summer school, this book presents an introduction to topics of current interest in the interface of geometry, topology and physics. It is aimed at graduate students in physics or mathematics with interests in geometric, algebraic as well as topological methods and their applications to quantum field theory. This volume contains the written notes corresponding to lectures given by experts in the field. They cover current topics of research in a way that is suitable for graduate students of mathematics or physics interested in the recent developments and interactions between geometry, topology and physics. The book also contains contributions by younger participants, displaying the ample range of topics treated in the school. A key feature of the present volume is the provision of a pedagogical presentation of rather advanced topics, in a way which is suitable for both mathematicians and physicists. Contents:Lectures:Spectral Geometry (B Iochum)Index Theory for Non-compact G-manifolds (M Braverman and L Cano)Generalized Euler Characteristics, Graph Hypersurfaces, and Feynman Periods (P Aluffi)Gravitation Theory and Chern-Simons Forms (J Zanelli)Noncommutative Geometry Models for Particle Physics (M Marcolli)Noncommutative Spacetimes and Quantum Physics (A P Balachandran)Integrability and the AdS/CFT Correspondence (M Staudacher)Compactifications of String Theory and Generalized Geometry (M Graña and H Triendl)Short Communications:Groupoids and Poisson Sigma Models with Boundary (A Cattaneo and I Contreras)A Survey on Orbifold String Topology (A Angel)Grothendieck Ring Class of Banana and Flower Graphs (P Morales-Almazán)On the Geometry Underlying a Real Lie Algebra Representation (R Vargas Le-Bert) Readership: Researchers in geometry and topology, mathematical physics. Keywords:Geometry;Topology;Geometric Methods;Quantum Field Theory;Renormalization;Index Theory;Noncommutative Geometry;Quantization;String Theory;Key Features:Unique style aimed at a mixed readership of mathematicians and physicistsIdeal for self-study or use in advanced courses or seminars
Author : Alexander Cardona,Hernan Ocampo,Sylvie Paycha
Publisher : World Scientific
Page : 500 pages
File Size : 47,7 Mb
Release : 2003
Category : Mathematics
ISBN : 9812705066
This volume offers an introduction to recent developments in several active topics of research at the interface between geometry, topology and quantum field theory. These include Hopf algebras underlying renormalization schemes in quantum field theory, noncommutative geometry with applications to index theory on one hand and the study of aperiodic solids on the other, geometry and topology of low dimensional manifolds with applications to topological field theory, Chern-Simons supergravity and the anti de Sitter/conformal field theory correspondence. It comprises seven lectures organized around three main topics, noncommutative geometry, topological field theory, followed by supergravity and string theory, complemented by some short communications by young participants of the school.
Author : Alexander Cardona,Iván Contreras,Andrés F. Reyes-Lega
Publisher : Cambridge University Press
Page : 395 pages
File Size : 46,8 Mb
Release : 2013-05-09
Category : Mathematics
ISBN : 9781107026834
A unique presentation of modern geometric methods in quantum field theory for researchers and graduate students in mathematics and physics.
Author : Alexander Cardona,Sylvie Paycha,Hernan Ocampo
Publisher : World Scientific
Page : 492 pages
File Size : 42,6 Mb
Release : 2003-03-21
Category : Mathematics
ISBN : 9789814487672
This volume offers an introduction to recent developments in several active topics of research at the interface between geometry, topology and quantum field theory. These include Hopf algebras underlying renormalization schemes in quantum field theory, noncommutative geometry with applications to index theory on one hand and the study of aperiodic solids on the other, geometry and topology of low dimensional manifolds with applications to topological field theory, Chern-Simons supergravity and the anti de Sitter/conformal field theory correspondence. It comprises seven lectures organized around three main topics, noncommutative geometry, topological field theory, followed by supergravity and string theory, complemented by some short communications by young participants of the school. Contents:Noncommutative Geometry:Hopf Algebras in Noncommutative Geometry (J C Várilly)The Noncommutative Geometry of Aperiodic Solids (J Bellissard)Noncommutative Geometry and Abstract Integration Theory (M-T Benameur)Topological Field Theory:Introduction to Quantum Invariants of 3-Manifolds, Topological Quantum Field Theories and Modular Categories (C Blanchet)An Introduction to Donaldson–Witten Theory (M Mariño)Supergravity and String Theory:(Super)-Gravities Beyond 4 Dimensions (J Zanelli)Introductory Lectures on String Theory and the AdS/CFT Correspondence (A Pankiewicz & S Theisen)Short Communications:Group Contractions and Its Consequences Upon Representations of Different Spatial Symmetry Groups (M Ayala-Sánchez & R W Haase)Phase Anomalies as Trace Anomalies in Chern–Simons Theory (A Cardona)Deligne Cohomology for Orbifolds, Discrete Torsion and B-Fields (E Lupercio & B Uribe) Readership: Graduate students and researchers in theoretical and mathematical physics, as well as geometry and topology. Keywords:
Author : Hernan Ocampo,Sylvie Paycha,Alexander Cardona
Publisher : World Scientific
Page : 495 pages
File Size : 47,6 Mb
Release : 2003
Category : Science
ISBN : 9789812381316
This volume offers an introduction to recent developments in several active topics of research at the interface between geometry, topology and quantum field theory. These include Hopf algebras underlying renormalization schemes in quantum field theory, noncommutative geometry with applications to index theory on one hand and the study of aperiodic solids on the other, geometry and topology of low dimensional manifolds with applications to topological field theory, Chern-Simons supergravity and the anti de Sitter/conformal field theory correspondence. It comprises seven lectures organized around three main topics, noncommutative geometry, topological field theory, followed by supergravity and string theory, complemented by some short communications by young participants of the school.
Author : Hans U. Boden
Publisher : American Mathematical Soc.
Page : 362 pages
File Size : 46,9 Mb
Release : 2005
Category : Manifolds (Mathematics)
ISBN : 9780821837245
This book contains expository papers that give an up-to-date account of recent developments and open problems in the geometry and topology of manifolds, along with several research articles that present new results appearing in published form for the first time. The unifying theme is the problem of understanding manifolds in low dimensions, notably in dimensions three and four, and the techniques include algebraic topology, surgery theory, Donaldson and Seiberg-Witten gauge theory,Heegaard Floer homology, contact and symplectic geometry, and Gromov-Witten invariants. The articles collected for this volume were contributed by participants of the Conference "Geometry and Topology of Manifolds" held at McMaster University on May 14-18, 2004 and are representative of the manyexcellent talks delivered at the conference.
Author : Eike Bick
Publisher : Springer Science & Business Media
Page : 380 pages
File Size : 44,8 Mb
Release : 2005-01-18
Category : Mathematics
ISBN : 3540231250
Application of the concepts and methods of topology and geometry have led to a deeper understanding of many crucial aspects in condensed matter physics, cosmology, gravity and particle physics. This book can be considered an advanced textbook on modern applications and recent developments in these fields of physical research. Written as a set of largely self-contained extensive lectures, the book gives an introduction to topological concepts in gauge theories, BRST quantization, chiral anomalies, supersymmetric solitons and noncommutative geometry. It will be of benefit to postgraduate students, educating newcomers to the field and lecturers looking for advanced material.
Author : Robert Friedman,John W. Morgan
Publisher : American Mathematical Soc.
Page : 233 pages
File Size : 40,9 Mb
Release : 1998
Category : Four-manifolds (Topology).
ISBN : 9780821805916
This text is part of the IAS/Park City Mathematics series and focuses on gauge theory and the topology of four-manifolds.
