Geometric Methods for Quantum Field Theory

Geometric Methods for Quantum Field Theory
Author: Hernan Ocampo,Sylvie Paycha,Andres Reyes
Publsiher: World Scientific
Total Pages: 528
Release: 2001-04-30
ISBN: 9814492825
Category: Science
Language: EN, FR, DE, ES & NL

Geometric Methods for Quantum Field Theory Book Excerpt:

Both mathematics and mathematical physics have many active areas of research where the interplay between geometry and quantum field theory has proved extremely fruitful. Duality, gauge field theory, geometric quantization, Seiberg–Witten theory, spectral properties and families of Dirac operators, and the geometry of loop groups offer some striking recent examples of modern topics which stand on the borderline between geometry and analysis on the one hand and quantum field theory on the other, where the physicist's and the mathematician's perspective complement each other, leading to new mathematical and physical concepts and results. This volume introduces the reader to some basic mathematical and physical tools and methods required to follow the recent developments in some active areas of mathematical physics, including duality, gauge field theory, geometric quantization, Seiberg-Witten theory, spectral properties and families of Dirac operators, and the geometry of loop groups. It comprises seven self-contained lectures, which should progressively give the reader a precise idea of some of the techniques used in these areas, as well as a few short communications presented by young participants at the school. Contents:Lectures:Introduction to Differentiable Manifolds and Symplectic Geometry (T Wurzbacher)Spectral Properties of the Dirac Operator and Geometrical Structures (O Hijazi)Quantum Theory of Fermion Systems: Topics Between Physics and Mathematics (E Langmann)Heat Equation and Spectral Geometry. Introduction for Beginners (K Wojciechowski)Renormalized Traces as a Geometric Tool (S Paycha)Concepts in Gauge Theory Leading to Electric-Magnetic Duality (T S Tsun)An Introduction to Seiberg-Witten Theory (H Ocampo)Short Communications:Remarks on Duality, Analytical Torsion and Gaussian Integration in Antisymmetric Field Theories (A Cardona)Multiplicative Anomaly for the ς-Regularized Determinant (C Ducourtioux)On Cohomogeneity One Riemannian Manifolds (S M B Kashani)A Differentiable Calculus on the Space of Loops and Connections (M Reiris)Quantum Hall Conductivity and Topological Invariants (A Reyes)Determinant of the Dirac Operator Over the Interval [0,β] (F Torres-Ardila) Readership: Mathematicians and physicists. Keywords:Reviews:“Many texts in theoretical physics do not contain a rigorous account of the mathematics they employ. However, this text does, and it omits no steps in the logic, thus making it very accessible to the mathematical community. Also it emphasizes physics, providing a link between the two disciplines which one rarely finds in a text.”Contemporary Physics

Geometric and Topological Methods for Quantum Field Theory

Geometric and Topological Methods for Quantum Field Theory
Author: Alexander Cardona,Iván Contreras,Andrés F. Reyes-Lega
Publsiher: Cambridge University Press
Total Pages: 383
Release: 2013-05-09
ISBN: 1107026830
Category: Science
Language: EN, FR, DE, ES & NL

Geometric and Topological Methods for Quantum Field Theory Book Excerpt:

"Based on lectures given at the renowed Villa de Leyva summer school, this book provides a unique presentation of modern geometric methods in quantum field theory. Written by experts, it enables readers to enter some of the most fascinating research topics in this subject. Covering a series of topics on geometry, topology, algebra, number theory methods and their applications to quantum field theory, the book covers topics such as Dirac structures, holomorphic bundles and stability, Feynman integrals, geometric aspects of quantum field theory and the standard model, spectral and Riemannian geometry and index theory. This is a valuable guide for graduate students and researchers in physics and mathematics wanting to enter this interesting research field at the borderline between mathematics and physics"--

Geometric Algebraic and Topological Methods for Quantum Field Theory

Geometric  Algebraic and Topological Methods for Quantum Field Theory
Author: Alexander Cardona,Carolina Neira-Jiménez,Hernán Ocampo,Sylvie Paycha,Andrés F Reyes-Lega
Publsiher: World Scientific
Total Pages: 380
Release: 2013-11-15
ISBN: 9814460060
Category: Mathematics
Language: EN, FR, DE, ES & NL

Geometric Algebraic and Topological Methods for Quantum Field Theory Book Excerpt:

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

Geometric and Topological Methods for Quantum Field Theory

Geometric and Topological Methods for Quantum Field Theory
Author: Alexander Cardona,Sylvie Paycha,Hernan Ocampo
Publsiher: World Scientific
Total Pages: 492
Release: 2003-03-21
ISBN: 9814487678
Category: Mathematics
Language: EN, FR, DE, ES & NL

Geometric and Topological Methods for Quantum Field Theory Book Excerpt:

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:

Geometric Algebraic and Topological Methods for Quantum Field Theory

Geometric  Algebraic and Topological Methods for Quantum Field Theory
Author: Leonardo Cano,Alexander Cardona,Hern Ocampo,Andr F Reyes Lega
Publsiher: World Scientific
Total Pages: 384
Release: 2016-09-06
ISBN: 9814730890
Category: Mathematics
Language: EN, FR, DE, ES & NL

Geometric Algebraic and Topological Methods for Quantum Field Theory Book Excerpt:

Based on lectures held at the 8th edition of the series of summer schools in Villa de Leyva since 1999, this book presents an introduction to topics of current interest at the interface of geometry, algebra, analysis, topology and theoretical physics. It is aimed at graduate students and researchers in physics or mathematics, and offers an introduction to the topics discussed in the two weeks of the summer school: operator algebras, conformal field theory, black holes, relativistic fluids, Lie groupoids and Lie algebroids, renormalization methods, spectral geometry and index theory for pseudo-differential operators.

Geometric Algebraic and Topological Methods for Quantum Field Theory

Geometric  Algebraic and Topological Methods for Quantum Field Theory
Author: Sylvie Payche
Publsiher: World Scientific
Total Pages: 378
Release: 2014
ISBN: 9814460052
Category: Science
Language: EN, FR, DE, ES & NL

Geometric Algebraic and Topological Methods for Quantum Field Theory Book Excerpt:

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.

Geometric and Topological Methods for Quantum Field Theory

Geometric and Topological Methods for Quantum Field Theory
Author: Hernan Ocampo,Eddy Pariguan,Sylvie Paycha
Publsiher: Cambridge University Press
Total Pages: 135
Release: 2010-04-29
ISBN: 113948673X
Category: Science
Language: EN, FR, DE, ES & NL

Geometric and Topological Methods for Quantum Field Theory Book Excerpt:

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.

Geometric and Topological Methods for Quantum Field Theory

Geometric and Topological Methods for Quantum Field Theory
Author: Bo Summer School Geometric and Topological Methods for Quantum
Publsiher: American Mathematical Soc.
Total Pages: 255
Release: 2007
ISBN: 0821840622
Category: Mathematics
Language: EN, FR, DE, ES & NL

Geometric and Topological Methods for Quantum Field Theory 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.

Differential Geometric Methods In Theoretical Physics Proceedings Of The Xx International Conference In 2 Volumes

Differential Geometric Methods In Theoretical Physics   Proceedings Of The Xx International Conference  In 2 Volumes
Author: Catto Sultan,Rocha Alvany
Publsiher: World Scientific
Total Pages: 1224
Release: 1992-01-27
ISBN: 9814555509
Category: Electronic Book
Language: EN, FR, DE, ES & NL

Differential Geometric Methods In Theoretical Physics Proceedings Of The Xx International Conference In 2 Volumes Book Excerpt:

This proceedings reports on some of the most recent advances on the interaction between Differential Geometry and Theoretical Physics, a very active and exciting area of contemporary research. The papers are grouped into the following four broad categories: Geometric Methods, Noncommutative Geometry, Quantum Gravity and Topological Quantum Field Theory. A few of the topics covered are Chern-Simons Theory and Generalizations, Knot Invariants, Models of 2D Gravity, Quantum Groups and Strings on Black Holes.

Differential Geometric Methods in Theoretical Physics

Differential Geometric Methods in Theoretical Physics
Author: Ling-Lie Chau,Werner Nahm
Publsiher: Springer Science & Business Media
Total Pages: 830
Release: 2013-06-29
ISBN: 1468491482
Category: Technology & Engineering
Language: EN, FR, DE, ES & NL

Differential Geometric Methods in Theoretical Physics Book Excerpt:

After several decades of reduced contact, the interaction between physicists and mathematicians in the front-line research of both fields recently became deep and fruit ful again. Many of the leading specialists of both fields became involved in this devel opment. This process even led to the discovery of previously unsuspected connections between various subfields of physics and mathematics. In mathematics this concerns in particular knots von Neumann algebras, Kac-Moody algebras, integrable non-linear partial differential equations, and differential geometry in low dimensions, most im portantly in three and four dimensional spaces. In physics it concerns gravity, string theory, integrable classical and quantum field theories, solitons and the statistical me chanics of surfaces. New discoveries in these fields are made at a rapid pace. This conference brought together active researchers in these areas, reporting their results and discussing with other participants to further develop thoughts in future new directions. The conference was attended by SO participants from 15 nations. These proceedings document the program and the talks at the conference. This conference was preceded by a two-week summer school. Ten lecturers gave extended lectures on related topics. The proceedings of the school will also be published in the NATO-AS[ volume by Plenum. The Editors vii ACKNOWLEDGMENTS We would like to thank the many people who have made the conference a success. Furthermore, ·we appreciate the excellent talks. The active participation of everyone present made the conference lively and stimulating. All of this made our efforts worth while.

Proceedings of the Summer School Geometric and Topological Methods for Quantum Field Theory

Proceedings of the Summer School Geometric and Topological Methods for Quantum Field Theory
Author: Alexander Cardona
Publsiher: World Scientific
Total Pages: 482
Release: 2003
ISBN: 9789812705068
Category: Algebraic topology
Language: EN, FR, DE, ES & NL

Proceedings of the Summer School Geometric and Topological Methods for Quantum Field Theory Book Excerpt:

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.

Geometric Approaches to Quantum Field Theory

Geometric Approaches to Quantum Field Theory
Author: Kieran Finn
Publsiher: Springer Nature
Total Pages: 135
Release: 2022
ISBN: 3030852695
Category: Electronic Book
Language: EN, FR, DE, ES & NL

Geometric Approaches to Quantum Field Theory Book Excerpt:

Geometric and Topological Methods for Quantum Field Theory

Geometric and Topological Methods for Quantum Field Theory
Author: Alexander Cardona
Publsiher: Unknown
Total Pages: 135
Release: 2013
ISBN: 9781107345577
Category: Geometric quantization
Language: EN, FR, DE, ES & NL

Geometric and Topological Methods for Quantum Field Theory Book Excerpt:

"Based on lectures given at the renowed Villa de Leyva summer school, this book provides a unique presentation of modern geometric methods in quantum field theory. Written by experts, it enables readers to enter some of the most fascinating research topics in this subject. Covering a series of topics on geometry, topology, algebra, number theory methods and their applications to quantum field theory, the book covers topics such as Dirac structures, holomorphic bundles and stability, Feynman integrals, geometric aspects of quantum field theory and the standard model, spectral and Riemannian geometry and index theory. This is a valuable guide for graduate students and researchers in physics and mathematics wanting to enter this interesting research field at the borderline between mathematics and physics"--

Geometric and Topological Methods for Quantum Field Theory

Geometric and Topological Methods for Quantum Field Theory
Author: Alexander Cardona. Iván Contreras. Andrés F. Reyes-Lega
Publsiher: Unknown
Total Pages: 135
Release: 2013
ISBN: 9781107357693
Category: Electronic Book
Language: EN, FR, DE, ES & NL

Geometric and Topological Methods for Quantum Field Theory Book Excerpt:

New Problems Methods and Techniques in Quantum Field Theory and Statistical Mechanics

New Problems  Methods and Techniques in Quantum Field Theory and Statistical Mechanics
Author: Mario Rasetti
Publsiher: World Scientific
Total Pages: 222
Release: 1990
ISBN: 9789810202255
Category: Science
Language: EN, FR, DE, ES & NL

New Problems Methods and Techniques in Quantum Field Theory and Statistical Mechanics Book Excerpt:

http://www.worldscientific.com/worldscibooks/10.1142/1095

Geometric Methods in Physics XXXVI

Geometric Methods in Physics XXXVI
Author: Piotr Kielanowski,Anatol Odzijewicz,Emma Previato
Publsiher: Springer
Total Pages: 425
Release: 2019-03-11
ISBN: 3030011569
Category: Mathematics
Language: EN, FR, DE, ES & NL

Geometric Methods in Physics XXXVI Book Excerpt:

This book collects papers based on the XXXVI Białowieża Workshop on Geometric Methods in Physics, 2017. The Workshop, which attracts a community of experts active at the crossroads of mathematics and physics, represents a major annual event in the field. Based on presentations given at the Workshop, the papers gathered here are previously unpublished, at the cutting edge of current research, and primarily grounded in geometry and analysis, with applications to classical and quantum physics. In addition, a Special Session was dedicated to S. Twareque Ali, a distinguished mathematical physicist at Concordia University, Montreal, who passed away in January 2016. For the past six years, the Białowieża Workshops have been complemented by a School on Geometry and Physics, comprising a series of advanced lectures for graduate students and early-career researchers. The extended abstracts of this year’s lecture series are also included here. The unique character of the Workshop-and-School series is due in part to the venue: a famous historical, cultural and environmental site in the Białowieża forest, a UNESCO World Heritage Centre in eastern Poland. Lectures are given in the Nature and Forest Museum, and local traditions are interwoven with the scientific activities.

Geometric and Algebraic Topological Methods in Quantum Mechanics

Geometric and Algebraic Topological Methods in Quantum Mechanics
Author: Giovanni Giachetta,Luigi Mangiarotti,Gennadi Sardanashvily
Publsiher: World Scientific
Total Pages: 720
Release: 2005-01-27
ISBN: 9814481149
Category: Science
Language: EN, FR, DE, ES & NL

Geometric and Algebraic Topological Methods in Quantum Mechanics Book Excerpt:

' In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry's geometric factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques based on the deep interplay between algebra, differential geometry and topology. The book aims at being a guide to advanced differential geometric and topological methods in quantum mechanics. Their main peculiarity lies in the fact that geometry in quantum theory speaks mainly the algebraic language of rings, modules, sheaves and categories. Geometry is by no means the primary scope of the book, but it underlies many ideas in modern quantum physics and provides the most advanced schemes of quantization. Contents:Commutative GeometryClassical Hamiltonian SystemsAlgebraic QuantizationGeometry of Algebraic QuantizationGeometric QuantizationSupergeometryDeformation QuantizationNon-Commutative GeometryGeometry of Quantum Groups Readership: Theoreticians and mathematicians of postgraduate and research level. Keywords:Algebraic Quantum Theory;Poisson Manifold;Hilbert Manifold;Geometric Quantization;Deformation Quantization;Supergeometry;Noncommutative Geometry;Constraint System;Quantum GroupKey Features:The book collects all the advanced methods of quantization in the last decadeIt presents in a compact way all the necessary up to date mathematical tools to be used in studying quantum problems.Reviews:“This book is well-written and I am convinced that it will be useful to all those interested in quantum theory.”Zentralblatt MATH “With respect to a propsective reader having a reasonably good background in mathematics, the notions, concepts, etc, are introduced in a self-contained but condensed manner … The book gives a very helpful supply of mathematical tools needed by a theoretical or mathematical physicist to effect entry into some of the new directions in theoretical physics. Also, a mathematician might appreciate the condensed presentation of definitions and results in one of the modern fields of mathematics for which one may be seeking an overview.”Mathematical Reviews '

Geometric Analysis and Applications to Quantum Field Theory

Geometric Analysis and Applications to Quantum Field Theory
Author: Peter Bouwknegt,Siye Wu
Publsiher: Springer Science & Business Media
Total Pages: 207
Release: 2012-12-06
ISBN: 1461200679
Category: Mathematics
Language: EN, FR, DE, ES & NL

Geometric Analysis and Applications to Quantum Field Theory Book Excerpt:

In the last decade there has been an extraordinary confluence of ideas in mathematics and theoretical physics brought about by pioneering discoveries in geometry and analysis. The various chapters in this volume, treating the interface of geometric analysis and mathematical physics, represent current research interests. No suitable succinct account of the material is available elsewhere. Key topics include: * A self-contained derivation of the partition function of Chern- Simons gauge theory in the semiclassical approximation (D.H. Adams) * Algebraic and geometric aspects of the Knizhnik-Zamolodchikov equations in conformal field theory (P. Bouwknegt) * Application of the representation theory of loop groups to simple models in quantum field theory and to certain integrable systems (A.L. Carey and E. Langmann) * A study of variational methods in Hermitian geometry from the viewpoint of the critical points of action functionals together with physical backgrounds (A. Harris) * A review of monopoles in nonabelian gauge theories (M.K. Murray) * Exciting developments in quantum cohomology (Y. Ruan) * The physics origin of Seiberg-Witten equations in 4-manifold theory (S. Wu) Graduate students, mathematicians and mathematical physicists in the above-mentioned areas will benefit from the user-friendly introductory style of each chapter as well as the comprehensive bibliographies provided for each topic. Prerequisite knowledge is minimal since sufficient background material motivates each chapter.

Differential Geometrical Methods in Theoretical Physics

Differential Geometrical Methods in Theoretical Physics
Author: K. Bleuler,M. Werner
Publsiher: Springer Science & Business Media
Total Pages: 471
Release: 2013-06-29
ISBN: 9401578095
Category: Mathematics
Language: EN, FR, DE, ES & NL

Differential Geometrical Methods in Theoretical Physics Book Excerpt:

Proceedings of the NATO Advanced Research Workshop and the 16th International Conference, Como, Italy, August 24-29, 1987

Differential Geometric Methods In Theoretical Physics Proceedings Of The Xxi International Conference

Differential Geometric Methods In Theoretical Physics   Proceedings Of The Xxi International Conference
Author: Yang Chen Ning,Ge Mo-lin,Zhou X W
Publsiher: World Scientific
Total Pages: 624
Release: 1993-07-31
ISBN: 9814553778
Category: Electronic Book
Language: EN, FR, DE, ES & NL

Differential Geometric Methods In Theoretical Physics Proceedings Of The Xxi International Conference Book Excerpt:

This book is to commemorate the 65th birthday of J J Giambiagi one of the most important Latin American physicists. Giambiagi, in collaboration with Bollini, invented the time-honoured Dimensional Regularization method in 1971. It includes contributions from many of his friends and former students, on their present fields of interest.