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Geometric and Topological Methods for Quantum Field Theory

2010-04-29 Science
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Release : 2010-04-29
Genre : Science
Kind : eBook
Book Rating : 73X/5 ( reviews)

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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. This book was released on 2010-04-29. 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.

Geometric Methods For Quantum Field Theory

2001-04-30 Science
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Release : 2001-04-30
Genre : Science
Kind : eBook
Book Rating : 825/5 ( reviews)

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Book Synopsis Geometric Methods For Quantum Field Theory by : Hernan Ocampo

Download or read book Geometric Methods For Quantum Field Theory written by Hernan Ocampo. This book was released on 2001-04-30. Available in PDF, EPUB and Kindle. 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.

Geometric Approaches to Quantum Field Theory

2021-10-07 Science
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Release : 2021-10-07
Genre : Science
Kind : eBook
Book Rating : 695/5 ( reviews)

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Book Synopsis Geometric Approaches to Quantum Field Theory by : Kieran Finn

Download or read book Geometric Approaches to Quantum Field Theory written by Kieran Finn. This book was released on 2021-10-07. Available in PDF, EPUB and Kindle. Book excerpt: The ancient Greeks believed that everything in the Universe should be describable in terms of geometry. This thesis takes several steps towards realising this goal by introducing geometric descriptions of systems such as quantum gravity, fermionic particles and the origins of the Universe itself. The author extends the applicability of previous work by Vilkovisky, DeWitt and others to include theories with spin 1⁄2 and spin 2 degrees of freedom. In addition, he introduces a geometric description of the potential term in a quantum field theory through a process known as the Eisenhart lift. Finally, the methods are applied to the theory of inflation, where they show how geometry can help answer a long-standing question about the initial conditions of the Universe. This publication is aimed at graduate and advanced undergraduate students and provides a pedagogical introduction to the exciting topic of field space covariance and the complete geometrization of quantum field theory.

Differential Geometric Methods in Theoretical Physics

2013-06-29 Technology & Engineering
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Release : 2013-06-29
Genre : Technology & Engineering
Kind : eBook
Book Rating : 482/5 ( reviews)

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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. This book was released on 2013-06-29. 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.

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

2003-03-21 Mathematics
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Release : 2003-03-21
Genre : Mathematics
Kind : eBook
Book Rating : 678/5 ( reviews)

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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. This book was released on 2003-03-21. 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.

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