Quantum Field Theory And Low Dimensional Geometry

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Low-Dimensional Topology and Quantum Field Theory

Author : Hugh Osborn
Publisher : Springer Science & Business Media
ISBN 13 : 1489916121
Total Pages : 318 pages
Book Rating : 4.4/5 (899 download)

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Book Synopsis Low-Dimensional Topology and Quantum Field Theory by : Hugh Osborn

Download or read book Low-Dimensional Topology and Quantum Field Theory written by Hugh Osborn and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: The motivations, goals and general culture of theoretical physics and mathematics are different. Most practitioners of either discipline have no necessity for most of the time to keep abreast of the latest developments in the other. However on occasion newly developed mathematical concepts become relevant in theoretical physics and the less rigorous theoretical physics framework may prove valuable in understanding and suggesting new theorems and approaches in pure mathematics. Such interdis ciplinary successes invariably cause much rejoicing, as over a prodigal son returned. In recent years the framework provided by quantum field theory and functional in tegrals, developed over half a century in theoretical physics, have proved a fertile soil for developments in low dimensional topology and especially knot theory. Given this background it was particularly pleasing that NATO was able to generously sup port an Advanced Research Workshop to be held in Cambridge, England from 6th to 12th September 1992 with the title Low Dimensional Topology and Quantum Field Theory. Although independently organised this overlapped as far as some speak ers were concerned with a longer term programme with the same title organised by Professor M Green, Professor E Corrigan and Dr R Lickorish. The contents of this proceedings of the workshop demonstrate the breadth of topics now of interest on the interface between theoretical physics and mathematics as well as the sophistication of the mathematical tools required in current theoretical physics.

Quantum Field Theory and Low-dimensional Geometry

Author : Michael Francis Atiyah
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (143 download)

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Book Synopsis Quantum Field Theory and Low-dimensional Geometry by : Michael Francis Atiyah

Download or read book Quantum Field Theory and Low-dimensional Geometry written by Michael Francis Atiyah and published by . This book was released on 1990 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Topology, Geometry, and Field Theory

Author :
Publisher :
ISBN 13 : 9789814534086
Total Pages : pages
Book Rating : 4.5/5 (34 download)

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Book Synopsis Topology, Geometry, and Field Theory by :

Download or read book Topology, Geometry, and Field Theory written by and published by . This book was released on 1994 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Geometric And Topological Methods For Quantum Field Theory - Proceedings Of The Summer School

Author : Alexander Cardona
Publisher : World Scientific
ISBN 13 : 9814487678
Total Pages : 495 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Geometric And Topological Methods For Quantum Field Theory - Proceedings Of The Summer School by : Alexander Cardona

Download or read book Geometric And Topological Methods For Quantum Field Theory - Proceedings Of The Summer School written by Alexander Cardona and published by World Scientific. This book was released on 2003-03-21 with total page 495 pages. Available in PDF, EPUB and Kindle. 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.

Lectures on Field Theory and Topology

Author : Daniel S. Freed
Publisher : American Mathematical Soc.
ISBN 13 : 1470452065
Total Pages : 186 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Lectures on Field Theory and Topology by : Daniel S. Freed

Download or read book Lectures on Field Theory and Topology written by Daniel S. Freed and published by American Mathematical Soc.. This book was released on 2019-08-23 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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

Author : Hernan Ocampo
Publisher : World Scientific
ISBN 13 : 9812381317
Total Pages : 495 pages
Book Rating : 4.8/5 (123 download)

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Book Synopsis Proceedings of the Summer School Geometric and Topological Methods for Quantum Field Theory by : Hernan Ocampo

Download or read book Proceedings of the Summer School Geometric and Topological Methods for Quantum Field Theory written by Hernan Ocampo and published by World Scientific. This book was released on 2003 with total page 495 pages. Available in PDF, EPUB and Kindle. 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.

Low-dimensional Quantum Field Theories for Condensed Matter Physicists

Author : Stig Lundqvist
Publisher : World Scientific Publishing Company Incorporated
ISBN 13 : 9789810221409
Total Pages : 611 pages
Book Rating : 4.2/5 (214 download)

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Book Synopsis Low-dimensional Quantum Field Theories for Condensed Matter Physicists by : Stig Lundqvist

Download or read book Low-dimensional Quantum Field Theories for Condensed Matter Physicists written by Stig Lundqvist and published by World Scientific Publishing Company Incorporated. This book was released on 1995 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a set of pedagogical reviews covering the most recent applications of low-dimensional quantum field theory in condensed matter physics, written by experts who have made major contributions to this rapidly developing field of research. The main purpose is to introduce active young researchers to new ideas and new techniques which are not covered by the standard textbooks

Geometric and Topological Methods for Quantum Field Theory

Author : Hernan Ocampo
Publisher : Cambridge University Press
ISBN 13 : 113948673X
Total Pages : 435 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Geometric and Topological Methods for Quantum Field Theory by : Hernan Ocampo

Download or read book Geometric and Topological Methods for Quantum Field Theory written by Hernan Ocampo and published by Cambridge University Press. This book was released on 2010-04-29 with total page 435 pages. Available in PDF, EPUB and Kindle. 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.

Low-Dimensional Applications of Quantum Field Theory

Author : L. Baulieu
Publisher :
ISBN 13 : 9781489919205
Total Pages : 388 pages
Book Rating : 4.9/5 (192 download)

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Book Synopsis Low-Dimensional Applications of Quantum Field Theory by : L. Baulieu

Download or read book Low-Dimensional Applications of Quantum Field Theory written by L. Baulieu and published by . This book was released on 2014-09-01 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Low-Dimensional Models in Statistical Physics and Quantum Field Theory

Author : Harald Grosse
Publisher : Springer
ISBN 13 :
Total Pages : 364 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Low-Dimensional Models in Statistical Physics and Quantum Field Theory by : Harald Grosse

Download or read book Low-Dimensional Models in Statistical Physics and Quantum Field Theory written by Harald Grosse and published by Springer. This book was released on 1996-03-18 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains thoroughly written reviews of modern developments in low-dimensional modelling of statistical mechanics and quantum systems. It addresses students as well as researchers. The main items can be grouped into integrable (quantum) spin systems, which lead in the continuum limit to (conformal invariant) quantum field theory models and their algebraic structures, ranging from the Yang-Baxter equation and quantum groups to noncommutative geometry.

Low-Dimensional Models in Statistical Physics and Quantum Field Theory

Author : Harald Grosse
Publisher : Springer
ISBN 13 : 9783662140673
Total Pages : 341 pages
Book Rating : 4.1/5 (46 download)

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Book Synopsis Low-Dimensional Models in Statistical Physics and Quantum Field Theory by : Harald Grosse

Download or read book Low-Dimensional Models in Statistical Physics and Quantum Field Theory written by Harald Grosse and published by Springer. This book was released on 2014-03-12 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains thoroughly written reviews of modern developments in low-dimensional modelling of statistical mechanics and quantum systems. It addresses students as well as researchers. The main items can be grouped into integrable (quantum) spin systems, which lead in the continuum limit to (conformal invariant) quantum field theory models and their algebraic structures, ranging from the Yang-Baxter equation and quantum groups to noncommutative geometry.

Geometry and Topology of Low Dimensional Systems

Author : Ramadevi Pichai
Publisher : Springer
ISBN 13 : 9783031595004
Total Pages : 0 pages
Book Rating : 4.5/5 (95 download)

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Book Synopsis Geometry and Topology of Low Dimensional Systems by : Ramadevi Pichai

Download or read book Geometry and Topology of Low Dimensional Systems written by Ramadevi Pichai and published by Springer. This book was released on 2024-07-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the field of topology, a branch of mathematics that explores the properties of geometric space, with a focus on low-dimensional systems. The authors discuss applications in various areas of physics. The first chapters of the book cover the formal aspects of topology, including classes, homotopic groups, metric spaces, and Riemannian and pseudo-Riemannian geometry. These topics are essential for understanding the theoretical concepts and notations used in the next chapters of the book. The applications encompass defects in crystalline structures, space topology, spin statistics, Braid group, Chern-Simons field theory, and 3D gravity, among others. This self-contained book provides all the necessary additional material for both physics and mathematics students. The presentation is enriched with examples and exercises, making it accessible for readers to grasp the concepts with ease. The authors adopt a pedagogical approach, posing many unsolved questions in simple situations that can serve as challenging projects for students. Suitable for a one-semester postgraduate level course, this text is ideal for teaching purposes.

Differential Geometric Methods in Theoretical Physics

Author : Ling-Lie Chau
Publisher : Springer Science & Business Media
ISBN 13 : 1468491482
Total Pages : 795 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Differential Geometric Methods in Theoretical Physics by : Ling-Lie Chau

Download or read book Differential Geometric Methods in Theoretical Physics written by Ling-Lie Chau and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 795 pages. Available in PDF, EPUB and Kindle. 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.

The Geometry and Physics of Knots

Author : Michael Francis Atiyah
Publisher : Cambridge University Press
ISBN 13 : 9780521395540
Total Pages : 112 pages
Book Rating : 4.3/5 (955 download)

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Book Synopsis The Geometry and Physics of Knots by : Michael Francis Atiyah

Download or read book The Geometry and Physics of Knots written by Michael Francis Atiyah and published by Cambridge University Press. This book was released on 1990-08-23 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes deal with an area that lies at the crossroads of mathematics and physics and rest primarily on the pioneering work of Vaughan Jones and Edward Witten, who related polynomial invariants of knots to a topological quantum field theory in 2+1 dimensions.

Low-Dimensional Applications of Quantum Field Theory

Author : L. Baulieu
Publisher : Springer Science & Business Media
ISBN 13 : 1489919198
Total Pages : 374 pages
Book Rating : 4.4/5 (899 download)

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Book Synopsis Low-Dimensional Applications of Quantum Field Theory by : L. Baulieu

Download or read book Low-Dimensional Applications of Quantum Field Theory written by L. Baulieu and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Cargese Summer School "Low Dimensional Applications of Quantum Field Theory" was held in July 1995. The School was dedicated to the memory of Claude Itzykson. This session focused on the recent progress in quantum field theory in two dimen sions with a particular emphasis on integrable models and applications of quantum field theory to condensed matter physics. A large fraction of the school was also devoted to a detailed review of the exciting developments in four dimensional super symmetric Yang-Mills theory. The diversity of the topics presented constitute, in our opinion, one of the most attractive features of these proceedings. Some contributions constitute a very thor ough introduction to their subject matter and should be helpful to advanced students in the field while others present entirely new research, not previously published, and should be of considerable interest to the specialist. There were in depth introductory lectures on the application of conformal field theory techniques to disordered systems, on the quantum Hall effect, on quantum in tegrable systems, on the thermodynamic Bethe Ansatz and on the new developments in supersymmetric gauges theories. The computation of the three point function of the Liouville model using conformal bootstrap methods was presented in detail.

An Introduction to Two-Dimensional Quantum Field Theory with (0,2) Supersymmetry

Author : Ilarion V. Melnikov
Publisher : Springer
ISBN 13 : 3030050858
Total Pages : 482 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis An Introduction to Two-Dimensional Quantum Field Theory with (0,2) Supersymmetry by : Ilarion V. Melnikov

Download or read book An Introduction to Two-Dimensional Quantum Field Theory with (0,2) Supersymmetry written by Ilarion V. Melnikov and published by Springer. This book was released on 2019-02-11 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces two-dimensional supersymmetric field theories with emphasis on both linear and non-linear sigma models. Complex differential geometry, in connection with supersymmetry, has played a key role in most developments of the last thirty years in quantum field theory and string theory. Both structures introduce a great deal of rigidity compared to the more general categories of non-supersymmetric theories and real differential geometry, allowing for many general conceptual results and detailed quantitative predictions. Two-dimensional (0,2) supersymmetric quantum field theories provide a natural arena for the fruitful interplay between geometry and quantum field theory. These theories play an important role in string theory and provide generalizations, still to be explored fully, of rich structures such as mirror symmetry. They also have applications to non-perturbative four-dimensional physics, for instance as descriptions of surface defects or low energy dynamics of solitonic strings in four-dimensional supersymmetric theories. The purpose of these lecture notes is to acquaint the reader with these fascinating theories, assuming a background in conformal theory, quantum field theory and differential geometry at the beginning graduate level. In order to investigate the profound relations between structures from complex geometry and field theory the text begins with a thorough examination of the basic structures of (0,2) quantum field theory and conformal field theory. Next, a simple class of Lagrangian theories, the (0,2) Landau-Ginzburg models, are discussed, together with the resulting renormalization group flows, dynamics, and symmetries. After a thorough introduction and examination of (0,2) non-linear sigma models, the text introduces linear sigma models that, in particular, provide a unified treatment of non-linear sigma models and Landau-Ginzburg theories. Many exercises, along with discussions of relevant mathematical notions and important open problems in the field, are included in the text.

Exact Methods in Low-dimensional Statistical Physics and Quantum Computing

Author : Stephane Ouvry
Publisher : Oxford University Press
ISBN 13 : 0199574618
Total Pages : 651 pages
Book Rating : 4.1/5 (995 download)

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Book Synopsis Exact Methods in Low-dimensional Statistical Physics and Quantum Computing by : Stephane Ouvry

Download or read book Exact Methods in Low-dimensional Statistical Physics and Quantum Computing written by Stephane Ouvry and published by Oxford University Press. This book was released on 2010-04-22 with total page 651 pages. Available in PDF, EPUB and Kindle. Book excerpt: Low-dimensional statistical models are instrumental in improving our understanding of emerging fields, such as quantum computing and cryptography, complex systems, and quantum fluids. This book of lectures by international leaders in the field sets these issues into a larger and more coherent theoretical perspective than is currently available.