Geometric Approaches To Quantum Field Theory

Author : Kieran Finn
Publisher : Springer Nature
Page : 212 pages
File Size : 54,5 Mb
Release : 2021-10-07
Category : Science
ISBN : 9783030852696

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Geometric Approaches to Quantum Field Theory by Kieran Finn Pdf

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.

Author : Frédéric Paugam
Publisher : Springer Science & Business Media
Page : 485 pages
File Size : 51,6 Mb
Release : 2014-02-20
Category : Science
ISBN : 9783319045641

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Towards the Mathematics of Quantum Field Theory by Frédéric Paugam Pdf

This ambitious and original book sets out to introduce to mathematicians (even including graduate students ) the mathematical methods of theoretical and experimental quantum field theory, with an emphasis on coordinate-free presentations of the mathematical objects in use. This in turn promotes the interaction between mathematicians and physicists by supplying a common and flexible language for the good of both communities, though mathematicians are the primary target. This reference work provides a coherent and complete mathematical toolbox for classical and quantum field theory, based on categorical and homotopical methods, representing an original contribution to the literature. The first part of the book introduces the mathematical methods needed to work with the physicists' spaces of fields, including parameterized and functional differential geometry, functorial analysis, and the homotopical geometric theory of non-linear partial differential equations, with applications to general gauge theories. The second part presents a large family of examples of classical field theories, both from experimental and theoretical physics, while the third part provides an introduction to quantum field theory, presents various renormalization methods, and discusses the quantization of factorization algebras.

Author : Hernan Ocampo,Eddy Pariguan,Sylvie Paycha
Publisher : Cambridge University Press
Page : 435 pages
File Size : 41,7 Mb
Release : 2010-04-29
Category : Science
ISBN : 9781139486736

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Geometric and Topological Methods for Quantum Field Theory by Hernan Ocampo,Eddy Pariguan,Sylvie Paycha Pdf

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 : Hernan Ocampo,Sylvie Paycha,Andres F Reyes-lega
Publisher : World Scientific
Page : 530 pages
File Size : 46,9 Mb
Release : 2001-04-30
Category : Science
ISBN : 9789814492829

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Geometric Methods For Quantum Field Theory by Hernan Ocampo,Sylvie Paycha,Andres F Reyes-lega Pdf

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.

Author : Dmitri Fursaev,Dmitri Vassilevich
Publisher : Springer Science & Business Media
Page : 294 pages
File Size : 42,6 Mb
Release : 2011-06-25
Category : Science
ISBN : 9789400702059

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Operators, Geometry and Quanta by Dmitri Fursaev,Dmitri Vassilevich Pdf

This book gives a detailed and self-contained introduction into the theory of spectral functions, with an emphasis on their applications to quantum field theory. All methods are illustrated with applications to specific physical problems from the forefront of current research, such as finite-temperature field theory, D-branes, quantum solitons and noncommutativity. In the first part of the book, necessary background information on differential geometry and quantization, including less standard material, is collected. The second part of the book contains a detailed description of main spectral functions and methods of their calculation. In the third part, the theory is applied to several examples (D-branes, quantum solitons, anomalies, noncommutativity). This book addresses advanced graduate students and researchers in mathematical physics with basic knowledge of quantum field theory and differential geometry. The aim is to prepare readers to use spectral functions in their own research, in particular in relation to heat kernels and zeta functions.

Author : Leonardo Cano,Alexander Cardona,Hern Ocampo,Andr F Reyes Lega
Publisher : World Scientific
Page : 384 pages
File Size : 48,8 Mb
Release : 2016-09-06
Category : Mathematics
ISBN : 9789814730891

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Geometric, Algebraic and Topological Methods for Quantum Field Theory by Leonardo Cano,Alexander Cardona,Hern Ocampo,Andr F Reyes Lega Pdf

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.

Author : Jan Ambjørn,Bergfinnur Durhuus,Þórður Jónsson
Publisher : Cambridge University Press
Page : 377 pages
File Size : 44,7 Mb
Release : 1997-06-19
Category : Science
ISBN : 9780521461672

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Quantum Geometry by Jan Ambjørn,Bergfinnur Durhuus,Þórður Jónsson Pdf

Describes random geometry and applications to strings, quantum gravity, topological field theory and membrane physics.

Author : Alexander Cardona,Iván Contreras,Andrés F. Reyes-Lega
Publisher : Cambridge University Press
Page : 128 pages
File Size : 50,5 Mb
Release : 2013-05-09
Category : Science
ISBN : 9781107355194

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Geometric and Topological Methods for Quantum Field Theory by Alexander Cardona,Iván Contreras,Andrés F. Reyes-Lega Pdf

Based on lectures given at the renowned 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.

Author : Gerhard Grensing
Publisher : World Scientific
Page : 1656 pages
File Size : 48,9 Mb
Release : 2021-07-15
Category : Science
ISBN : 9789811237096

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Structural Aspects Of Quantum Field Theory And Noncommutative Geometry (Second Edition) (In 2 Volumes) by Gerhard Grensing Pdf

The book is devoted to the subject of quantum field theory. It is divided into two volumes. The first volume can serve as a textbook on main techniques and results of quantum field theory, while the second treats more recent developments, in particular the subject of quantum groups and noncommutative geometry, and their interrelation.The second edition is extended by additional material, mostly concerning the impact of noncommutative geometry on theories beyond the standard model of particle physics, especially the possible role of torsion in the context of the dark matter problem. Furthermore, the text includes a discussion of the Randall-Sundrum model and the Seiberg-Witten equations.

Author : Sylvie Payche
Publisher : World Scientific
Page : 378 pages
File Size : 54,9 Mb
Release : 2014
Category : Science
ISBN : 9789814460057

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Geometric, Algebraic and Topological Methods for Quantum Field Theory by Sylvie Payche 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.

Author : Daniel Canarutto
Publisher : Oxford University Press, USA
Page : 362 pages
File Size : 53,8 Mb
Release : 2020-10-05
Category : Mathematics
ISBN : 9780198861492

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Gauge Field Theory in Natural Geometric Language by Daniel Canarutto Pdf

Gauge Field theory in Natural Geometric Language addresses the need to clarify basic mathematical concepts at the crossroad between gravitation and quantum physics. Selected mathematical and theoretical topics are exposed within a brief, integrated approach that exploits standard and non-standard notions, as well as recent advances, in a natural geometric language in which the role of structure groups can be regarded as secondary even in the treatment of the gauge fields themselves. In proposing an original bridge between physics and mathematics, this text will appeal not only to mathematicians who wish to understand some of the basic ideas involved in quantum particle physics, but also to physicists who are not satisfied with the usual mathematical presentations of their field.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 50,5 Mb
Release : 1994
Category : Electronic
ISBN : 9994437860

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Geometry and Quantum Field Theory by Anonim Pdf

Author : Eberhard Zeidler
Publisher : Springer Science & Business Media
Page : 1060 pages
File Size : 45,7 Mb
Release : 2007-04-18
Category : Science
ISBN : 9783540347644

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Quantum Field Theory I: Basics in Mathematics and Physics by Eberhard Zeidler Pdf

This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists, at levels ranging from advanced undergraduate students to professional scientists. The book bridges the acknowledged gap between the different languages used by mathematicians and physicists. For students of mathematics the author shows that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which goes beyond the usual curriculum in physics.

Author : Alexander Cardona,Hernan Ocampo,Sylvie Paycha
Publisher : World Scientific
Page : 500 pages
File Size : 50,7 Mb
Release : 2003
Category : Mathematics
ISBN : 9812705066

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

Author : Charles Nash
Publisher : Elsevier
Page : 404 pages
File Size : 45,9 Mb
Release : 1991
Category : Mathematics
ISBN : 0125140762

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Differential Topology and Quantum Field Theory by Charles Nash Pdf

The remarkable developments in differential topology and how these recent advances have been applied as a primary research tool in quantum field theory are presented here in a style reflecting the genuinely two-sided interaction between mathematical physics and applied mathematics. The author, following his previous work (Nash/Sen: Differential Topology for Physicists, Academic Press, 1983), covers elliptic differential and pseudo-differential operators, Atiyah-Singer index theory, topological quantum field theory, string theory, and knot theory. The explanatory approach serves to illuminate and clarify these theories for graduate students and research workers entering the field for the first time. Treats differential geometry, differential topology, and quantum field theory Includes elliptic differential and pseudo-differential operators, Atiyah-Singer index theory, topological quantum field theory, string theory, and knot theory Tackles problems of quantum field theory using differential topology as a tool