Lectures On Field Theory And Topology

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Lectures on Field Theory and Topology

Daniel S. Freed
Lectures on Field Theory and Topology Book PDF

Author : Daniel S. Freed
Publisher : American Mathematical Soc.
Page : 186 pages
File Size : 44,6 Mb
Release : 2019-08-23
Category : Algebraic topology
ISBN : 9781470452063

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Lectures on Field Theory and Topology by Daniel S. Freed Pdf

These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.

Lectures on Field Theory and Topology

Daniel S. Freed
Lectures on Field Theory and Topology Book PDF

Author : Daniel S. Freed
Publisher : Unknown
Page : 202 pages
File Size : 42,8 Mb
Release : 2019
Category : Algebraic topology
ISBN : 1470453916

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Lectures on Field Theory and Topology by Daniel S. Freed Pdf

These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory.

Lectures on Factorization Homology, ∞-Categories, and Topological Field Theories

Hiro Lee Tanaka
Lectures on Factorization Homology Categories and Topological Field Theories Book PDF

Author : Hiro Lee Tanaka
Publisher : Springer Nature
Page : 84 pages
File Size : 44,7 Mb
Release : 2020-12-14
Category : Science
ISBN : 9783030611637

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Lectures on Factorization Homology, ∞-Categories, and Topological Field Theories by Hiro Lee Tanaka Pdf

This book provides an informal and geodesic introduction to factorization homology, focusing on providing intuition through simple examples. Along the way, the reader is also introduced to modern ideas in homotopy theory and category theory, particularly as it relates to the use of infinity-categories. As with the original lectures, the text is meant to be a leisurely read suitable for advanced graduate students and interested researchers in topology and adjacent fields.

Geometric and Topological Methods for Quantum Field Theory

Sylvie Paycha
Geometric and Topological Methods for Quantum Field Theory Book PDF

Author : Sylvie Paycha
Publisher : American Mathematical Soc.
Page : 272 pages
File Size : 43,5 Mb
Release : 2007
Category : Algebraic topology
ISBN : 9780821840627

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Geometric and Topological Methods for Quantum Field Theory by Sylvie Paycha Pdf

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.

Geometric and Topological Methods for Quantum Field Theory

Hernan Ocampo,Sylvie Paycha,Andrés Vargas
Geometric and Topological Methods for Quantum Field Theory Book PDF

Author : Hernan Ocampo,Sylvie Paycha,Andrés Vargas
Publisher : Springer
Page : 230 pages
File Size : 45,5 Mb
Release : 2009-09-02
Category : Science
ISBN : 3540806679

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Geometric and Topological Methods for Quantum Field Theory by Hernan Ocampo,Sylvie Paycha,Andrés Vargas Pdf

This volume offers an introduction, in the form of four extensive lectures, to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. The first lecture is by Christine Lescop on knot invariants and configuration spaces, in which a universal finite-type invariant for knots is constructed as a series of integrals over configuration spaces. This is followed by the contribution of Raimar Wulkenhaar on Euclidean quantum field theory from a statistical point of view. The author also discusses possible renormalization techniques on noncommutative spaces. The third lecture is by Anamaria Font and Stefan Theisen on string compactification with unbroken supersymmetry. The authors show that this requirement leads to internal spaces of special holonomy and describe Calabi-Yau manifolds in detail. The last lecture, by Thierry Fack, is devoted to a K-theory proof of the Atiyah-Singer index theorem and discusses some applications of K-theory to noncommutative geometry. These lectures notes, which are aimed in particular at graduate students in physics and mathematics, start with introductory material before presenting more advanced results. Each chapter is self-contained and can be read independently.

Geometric, Algebraic and Topological Methods for Quantum Field Theory

Alexander Cardona,Carolina Neira-Jiménez,Hernán Ocampo,Sylvie Paycha,Andrés F Reyes-Lega
Geometric Algebraic and Topological Methods for Quantum Field Theory Book PDF

Author : Alexander Cardona,Carolina Neira-Jiménez,Hernán Ocampo,Sylvie Paycha,Andrés F Reyes-Lega
Publisher : World Scientific
Page : 380 pages
File Size : 46,6 Mb
Release : 2013-11-15
Category : Mathematics
ISBN : 9789814460064

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Geometric, Algebraic and Topological Methods for Quantum Field Theory by Alexander Cardona,Carolina Neira-Jiménez,Hernán Ocampo,Sylvie Paycha,Andrés F Reyes-Lega Pdf

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

Monoidal Categories and Topological Field Theory

Vladimir Turaev,Alexis Virelizier
Monoidal Categories and Topological Field Theory Book PDF

Author : Vladimir Turaev,Alexis Virelizier
Publisher : Birkhäuser
Page : 523 pages
File Size : 45,6 Mb
Release : 2017-06-28
Category : Mathematics
ISBN : 9783319498348

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Monoidal Categories and Topological Field Theory by Vladimir Turaev,Alexis Virelizier Pdf

This monograph is devoted to monoidal categories and their connections with 3-dimensional topological field theories. Starting with basic definitions, it proceeds to the forefront of current research. Part 1 introduces monoidal categories and several of their classes, including rigid, pivotal, spherical, fusion, braided, and modular categories. It then presents deep theorems of Müger on the center of a pivotal fusion category. These theorems are proved in Part 2 using the theory of Hopf monads. In Part 3 the authors define the notion of a topological quantum field theory (TQFT) and construct a Turaev-Viro-type 3-dimensional state sum TQFT from a spherical fusion category. Lastly, in Part 4 this construction is extended to 3-manifolds with colored ribbon graphs, yielding a so-called graph TQFT (and, consequently, a 3-2-1 extended TQFT). The authors then prove the main result of the monograph: the state sum graph TQFT derived from any spherical fusion category is isomorphic to the Reshetikhin-Turaev surgery graph TQFT derived from the center of that category. The book is of interest to researchers and students studying topological field theory, monoidal categories, Hopf algebras and Hopf monads.

Topology, Geometry And Field Theory - Proceedings Of The 31st International Taniguchi Symposium And Proceedings Of The Conference

Kenji Fukaya,Dieter Kotschick,M Furuta,Toshitake Kohno
Topology Geometry And Field Theory Proceedings Of The 31st International Taniguchi Symposium And Proceedings Of The Conference Book PDF

Author : Kenji Fukaya,Dieter Kotschick,M Furuta,Toshitake Kohno
Publisher : World Scientific
Page : 266 pages
File Size : 43,9 Mb
Release : 1994-08-31
Category : Electronic
ISBN : 9789814550642

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Topology, Geometry And Field Theory - Proceedings Of The 31st International Taniguchi Symposium And Proceedings Of The Conference by Kenji Fukaya,Dieter Kotschick,M Furuta,Toshitake Kohno Pdf

Nobel Symposium 129 on Neutrino Physics was held at Haga Slott in Enköping, Sweden during August 19-24, 2004. Invited to the symposium were around 40 globally leading researchers in the field of neutrino physics, both experimental and theoretical.The dominant theme of the lectures was neutrino oscillations, which after several years were recently verified by results from the Super-Kamiokande detector in Kamioka, Japan and the SNO detector in Sudbury, Canada. Discussion focused especially on effects of neutrino oscillations derived from the presence of matter and the fact that three different neutrinos exist. Since neutrino oscillations imply that neutrinos have mass, this is the first experimental observation that fundamentally deviates from the standard model of particle physics. This is a challenge to both theoretical and experimental physics. The various oscillation parameters will be determined with increased precision in new, specially designed experiments. Theoretical physics is working intensively to insert the knowledge that neutrinos have mass into the theoretical models that describe particle physics. The lectures provided a very good description of the intensive situation in the field right now. The topics discussed also included mass models for neutrinos, neutrinos in extra dimensions as well as the “seesaw mechanism,” which provides a good description of why neutrino masses are so small.This book is A4 size and in full color.

Quantum Field Theory and Manifold Invariants

Daniel S. Freed,Sergei Gukov,Ciprian Manolescu,Constantin Teleman,Ulrike Tillmann
Quantum Field Theory and Manifold Invariants Book PDF

Author : Daniel S. Freed,Sergei Gukov,Ciprian Manolescu,Constantin Teleman,Ulrike Tillmann
Publisher : American Mathematical Society, IAS/Park City Mathematics Institute
Page : 476 pages
File Size : 50,7 Mb
Release : 2021-12-02
Category : Mathematics
ISBN : 9781470461232

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Quantum Field Theory and Manifold Invariants by Daniel S. Freed,Sergei Gukov,Ciprian Manolescu,Constantin Teleman,Ulrike Tillmann Pdf

This volume contains lectures from the Graduate Summer School “Quantum Field Theory and Manifold Invariants” held at Park City Mathematics Institute 2019. The lectures span topics in topology, global analysis, and physics, and they range from introductory to cutting edge. Topics treated include mathematical gauge theory (anti-self-dual equations, Seiberg-Witten equations, Higgs bundles), classical and categorified knot invariants (Khovanov homology, Heegaard Floer homology), instanton Floer homology, invertible topological field theory, BPS states and spectral networks. This collection presents a rich blend of geometry and topology, with some theoretical physics thrown in as well, and so provides a snapshot of a vibrant and fast-moving field. Graduate students with basic preparation in topology and geometry can use this volume to learn advanced background material before being brought to the frontiers of current developments. Seasoned researchers will also benefit from the systematic presentation of exciting new advances by leaders in their fields.

Selected Topics on the General Properties of Quantum Field Theory

F. Strocchi
Selected Topics on the General Properties of Quantum Field Theory Book PDF

Author : F. Strocchi
Publisher : World Scientific
Page : 194 pages
File Size : 49,9 Mb
Release : 1993
Category : Science
ISBN : 981021149X

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Selected Topics on the General Properties of Quantum Field Theory by F. Strocchi Pdf

This book provides a readable account of the foundations of QFT, in particular of the Euclidean formulation with emphasis on the interplay between physical requirements and mathematical structures. The general structures underlying the conventional local (renormalizable) formulation of gauge QFT are discussed also on the basis of simple models. The mechanism of confinement, non-trivial topology and ?-vacua, chiral symmetry breaking and solution of the U(1) problem are clarified through a careful analysis of the Schwinger model, which settles unclear or debated points.

Geometry and Quantum Field Theory

Daniel S. Freed,Karen K. Uhlenbeck,American Mathematical Society,Institute for Advanced Study (Princeton, N.J.)
Geometry and Quantum Field Theory Book PDF

Author : Daniel S. Freed,Karen K. Uhlenbeck,American Mathematical Society,Institute for Advanced Study (Princeton, N.J.)
Publisher : American Mathematical Soc.
Page : 476 pages
File Size : 41,7 Mb
Release : 1995
Category : Science
ISBN : 0821886835

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Geometry and Quantum Field Theory by Daniel S. Freed,Karen K. Uhlenbeck,American Mathematical Society,Institute for Advanced Study (Princeton, N.J.) Pdf

The first title in a new series, this book explores topics from classical and quantum mechanics and field theory. The material is presented at a level between that of a textbook and research papers making it ideal for graduate students. The book provides an entree into a field that promises to remain exciting and important for years to come.

Lectures on Tensor Categories and Modular Functors

Bojko Bakalov,Alexander A. Kirillov
Lectures on Tensor Categories and Modular Functors Book PDF

Author : Bojko Bakalov,Alexander A. Kirillov
Publisher : American Mathematical Soc.
Page : 232 pages
File Size : 42,8 Mb
Release : 2001
Category : Abelian categories
ISBN : 9780821826867

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Lectures on Tensor Categories and Modular Functors by Bojko Bakalov,Alexander A. Kirillov Pdf

This book gives an exposition of the relations among the following three topics: monoidal tensor categories (such as a category of representations of a quantum group), 3-dimensional topological quantum field theory, and 2-dimensional modular functors (which naturally arise in 2-dimensional conformal field theory). The following examples are discussed in detail: the category of representations of a quantum group at a root of unity and the Wess-Zumino-Witten modular functor. The idea that these topics are related first appeared in the physics literature in the study of quantum field theory. Pioneering works of Witten and Moore-Seiberg triggered an avalanche of papers, both physical and mathematical, exploring various aspects of these relations. Upon preparing to lecture on the topic at MIT, however, the authors discovered that the existing literature was difficult and that there were gaps to fill. The text is wholly expository and finely succinct. It gathers results, fills existing gaps, and simplifies some proofs. The book makes an important addition to the existing literature on the topic. It would be suitable as a course text at the advanced-graduate level.

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

Hernan Ocampo,Sylvie Paycha,Alexander Cardona
Proceedings of the Summer School Geometric and Topological Methods for Quantum Field Theory Book PDF

Author : Hernan Ocampo,Sylvie Paycha,Alexander Cardona
Publisher : World Scientific
Page : 495 pages
File Size : 45,7 Mb
Release : 2003
Category : Science
ISBN : 9789812381316

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Proceedings of the Summer School Geometric and Topological Methods for Quantum Field Theory by Hernan Ocampo,Sylvie Paycha,Alexander Cardona Pdf

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.

Topological Quantum Field Theories and Geometry of Loop Spaces

L Fehér,J Szenthe,A Stipsicz
Topological Quantum Field Theories and Geometry of Loop Spaces Book PDF

Author : L Fehér,J Szenthe,A Stipsicz
Publisher : World Scientific
Page : 124 pages
File Size : 51,6 Mb
Release : 1992-10-09
Category : Electronic
ISBN : 9789814553957

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Topological Quantum Field Theories and Geometry of Loop Spaces by L Fehér,J Szenthe,A Stipsicz Pdf

These lectures introduce some very popular fields in topology. The topics discussed are interrelated with modern physics and include works of four leading researchers: M Atiyah, R Bott, J Jones and G Segal. The original lectures presented at the conference at Budapest are enlarged with appendices to make these notes self-contained. Contents:A New Knot Invariant I (M F Atiyah)A New Knot Invariant II: Topological Quantum Field Theories and the Jones Polynomial (M F Atiyah)Representations of Loop Groups I: Factorization Theorems (G Segal)Representations of Loop Groups II: The Determinant Bundle (G Segal)Topological Quantum Field Theories with Finite Groups (G Segal)The Index Theorem and Differential Forms on Loop Spaces (J D S Jones)Topological Aspects of Loop Groups (R Bott)Appendices: Spin Structures and Dirac OperatorsThe Wiener Integral and the Feynman-Kac FormulaTopological Quantum Field TheoriesBorel-Weil Theory Readership: Mathematicians and mathematical physicists. keywords:

Quantum Field Theory and Noncommutative Geometry

Ursula Carow-Watamura,Yoshiaki Maeda
Quantum Field Theory and Noncommutative Geometry Book PDF

Author : Ursula Carow-Watamura,Yoshiaki Maeda
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 41,7 Mb
Release : 2005-02-21
Category : Mathematics
ISBN : 3540239006

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Quantum Field Theory and Noncommutative Geometry by Ursula Carow-Watamura,Yoshiaki Maeda Pdf

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.