Geometry And Quantum Field Theory

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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 : 43,6 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.

Geometric Approaches to Quantum Field Theory

Kieran Finn
Geometric Approaches to Quantum Field Theory Book PDF

Author : Kieran Finn
Publisher : Springer Nature
Page : 212 pages
File Size : 55,8 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.

Topology, Geometry and Quantum Field Theory

Ulrike Luise Tillmann
Topology Geometry and Quantum Field Theory Book PDF

Author : Ulrike Luise Tillmann
Publisher : Cambridge University Press
Page : 596 pages
File Size : 44,8 Mb
Release : 2004-06-28
Category : Mathematics
ISBN : 0521540496

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Topology, Geometry and Quantum Field Theory by Ulrike Luise Tillmann Pdf

The symposium held in honour of the 60th birthday of Graeme Segal brought together leading physicists and mathematicians. Its topics were centred around string theory, M-theory, and quantum gravity on the one hand, and K-theory, elliptic cohomology, quantum cohomology and string topology on the other. Geometry and quantum physics developed in parallel since the recognition of the central role of non-abelian gauge theory in elementary particle physics in the late seventies and the emerging study of super-symmetry and string theory. With its selection of survey and research articles these proceedings fulfil the dual role of reporting on developments in the field and defining directions for future research. For the first time Graeme Segal's manuscript 'The definition of Conformal Field Theory' is published, which has been greatly influential over more than ten years. An introduction by the author puts it into the present context.

Geometric and Topological Methods for Quantum Field Theory

Hernan Ocampo,Eddy Pariguan,Sylvie Paycha
Geometric and Topological Methods for Quantum Field Theory Book PDF

Author : Hernan Ocampo,Eddy Pariguan,Sylvie Paycha
Publisher : Cambridge University Press
Page : 435 pages
File Size : 47,7 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.

Geometry and Quantum Field Theory

Daniel S. Freed,Karen K. Uhlenbeck
Geometry and Quantum Field Theory Book PDF

Author : Daniel S. Freed,Karen K. Uhlenbeck
Publisher : American Mathematical Soc.
Page : 472 pages
File Size : 41,8 Mb
Release : 1995
Category : Science
ISBN : 9780821804001

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Geometry and Quantum Field Theory by Daniel S. Freed,Karen K. Uhlenbeck Pdf

Exploring topics from classical and quantum mechnanics and field theory, this book is based on lectures presented in the Graduate Summer School at the Regional Geometry Institute in Park City, Utah, in 1991. The chapter by Bryant treats Lie groups and symplectic geometry, examining not only the connection with mechanics but also the application to differential equations and the recent work of the Gromov school. Rabin's discussion of quantum mechanics and field theory is specifically aimed at mathematicians. Alvarez describes the application of supersymmetry to prove the Atiyah-Singer index theorem, touching on ideas that also underlie more complicated applications of supersymmetry. Quinn's account of the topological quantum field theory captures the formal aspects of the path integral and shows how these ideas can influence branches of mathematics which at first glance may not seem connected. Presenting material at a level between that of textbooks and research papers, much of the book would provide excellent material for graduate courses. The book provides an entree into a field that promises to remain exciting and important for years to come.

Noncommutative Geometry, Quantum Fields and Motives

Alain Connes,Matilde Marcolli
Noncommutative Geometry Quantum Fields and Motives Book PDF

Author : Alain Connes,Matilde Marcolli
Publisher : American Mathematical Soc.
Page : 785 pages
File Size : 49,9 Mb
Release : 2019-03-13
Category : Electronic
ISBN : 9781470450458

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Noncommutative Geometry, Quantum Fields and Motives by Alain Connes,Matilde Marcolli Pdf

The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book deals with quantum field theory and the geometric structure of renormalization as a Riemann-Hilbert correspondence. It also presents a model of elementary particle physics based on noncommutative geometry. The main result is a complete derivation of the full Standard Model Lagrangian from a very simple mathematical input. Other topics covered in the first part of the book are a noncommutative geometry model of dimensional regularization and its role in anomaly computations, and a brief introduction to motives and their conjectural relation to quantum field theory. The second part of the book gives an interpretation of the Weil explicit formula as a trace formula and a spectral realization of the zeros of the Riemann zeta function. This is based on the noncommutative geometry of the adèle class space, which is also described as the space of commensurability classes of Q-lattices, and is dual to a noncommutative motive (endomotive) whose cyclic homology provides a general setting for spectral realizations of zeros of L-functions. The quantum statistical mechanics of the space of Q-lattices, in one and two dimensions, exhibits spontaneous symmetry breaking. In the low-temperature regime, the equilibrium states of the corresponding systems are related to points of classical moduli spaces and the symmetries to the class field theory of the field of rational numbers and of imaginary quadratic fields, as well as to the automorphisms of the field of modular functions. The book ends with a set of analogies between the noncommutative geometries underlying the mathematical formulation of the Standard Model minimally coupled to gravity and the moduli spaces of Q-lattices used in the study of the zeta function.

Differential Topology and Quantum Field Theory

Charles Nash
Differential Topology and Quantum Field Theory Book PDF

Author : Charles Nash
Publisher : Elsevier
Page : 404 pages
File Size : 53,9 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

Quantum Mechanics, Quantum Field Theory

R. Mirman
Quantum Mechanics Quantum Field Theory Book PDF

Author : R. Mirman
Publisher : iUniverse
Page : 341 pages
File Size : 43,7 Mb
Release : 2004-12
Category : Quantum field theory
ISBN : 9780595336906

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Quantum Mechanics, Quantum Field Theory by R. Mirman Pdf

The author does not want a book description on the back cover.

Symplectic Geometry and Quantum Mechanics

Maurice A. de Gosson
Symplectic Geometry and Quantum Mechanics Book PDF

Author : Maurice A. de Gosson
Publisher : Springer Science & Business Media
Page : 375 pages
File Size : 43,6 Mb
Release : 2006-08-06
Category : Mathematics
ISBN : 9783764375751

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Symplectic Geometry and Quantum Mechanics by Maurice A. de Gosson Pdf

This book offers a complete discussion of techniques and topics intervening in the mathematical treatment of quantum and semi-classical mechanics. It starts with a very readable introduction to symplectic geometry. Many topics are also of genuine interest for pure mathematicians working in geometry and topology.

Operators, Geometry and Quanta

Dmitri Fursaev,Dmitri Vassilevich
Operators Geometry and Quanta Book PDF

Author : Dmitri Fursaev,Dmitri Vassilevich
Publisher : Springer Science & Business Media
Page : 294 pages
File Size : 42,8 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.

Geometric Methods for Quantum Field Theory

Hernan Ocampo,Sylvie Paycha,Andres Reyes
Geometric Methods for Quantum Field Theory Book PDF

Author : Hernan Ocampo,Sylvie Paycha,Andres Reyes
Publisher : World Scientific
Page : 530 pages
File Size : 52,9 Mb
Release : 2001
Category : Science
ISBN : 9789810243517

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Geometric Methods for Quantum Field Theory by Hernan Ocampo,Sylvie Paycha,Andres Reyes 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.

Quantum Geometry

Jan Ambjørn,Bergfinnur Durhuus,Þórður Jónsson
Quantum Geometry Book PDF

Author : Jan Ambjørn,Bergfinnur Durhuus,Þórður Jónsson
Publisher : Cambridge University Press
Page : 377 pages
File Size : 40,6 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.

Geometric Methods For Quantum Field Theory

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

Author : Hernan Ocampo,Sylvie Paycha,Andres F Reyes-lega
Publisher : World Scientific
Page : 530 pages
File Size : 41,5 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.

Quantum Geometry

Margaret Prugovecki
Quantum Geometry Book PDF

Author : Margaret Prugovecki
Publisher : Springer Science & Business Media
Page : 543 pages
File Size : 52,8 Mb
Release : 2013-03-14
Category : Science
ISBN : 9789401579711

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Quantum Geometry by Margaret Prugovecki Pdf

This monograph presents a review and analysis of the main mathematical, physical and epistomological difficulties encountered at the foundational level by all the conventional formulations of relativistic quantum theories, ranging from relativistic quantum mechanics and quantum field theory in Minkowski space, to the various canonical and covariant approaches to quantum gravity. It is, however, primarily devoted to the systematic presentation of a quantum framework meant to deal effectively with these difficulties by reconsidering the foundations of these subjects, analyzing their epistemic nature, and then developing mathematical tools which are specifically designed for the elimination of all the basic inconsistencies. A carefully documented historical survey is included, and additional extensive notes containing quotations from original sources are incorporated at the end of each chapter, so that the reader will be brought up-to-date with the very latest developments in quantum field theory in curved spacetime, quantum gravity and quantum cosmology. The survey further provides a backdrop against which the new foundational and mathematical ideas of the present approach to these subjects can be brought out in sharper relief.

Towards the Mathematics of Quantum Field Theory

Frédéric Paugam
Towards the Mathematics of Quantum Field Theory Book PDF

Author : Frédéric Paugam
Publisher : Springer Science & Business Media
Page : 485 pages
File Size : 47,8 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.