Quantum Field Theory And Topology

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Quantum Field Theory and Topology

Author : Albert S. Schwarz
Publisher : Springer Science & Business Media
ISBN 13 : 366202943X
Total Pages : 277 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Quantum Field Theory and Topology by : Albert S. Schwarz

Download or read book Quantum Field Theory and Topology written by Albert S. Schwarz and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years topology has firmly established itself as an important part of the physicist's mathematical arsenal. It has many applications, first of all in quantum field theory, but increasingly also in other areas of physics. The main focus of this book is on the results of quantum field theory that are obtained by topological methods. Some aspects of the theory of condensed matter are also discussed. Part I is an introduction to quantum field theory: it discusses the basic Lagrangians used in the theory of elementary particles. Part II is devoted to the applications of topology to quantum field theory. Part III covers the necessary mathematical background in summary form. The book is aimed at physicists interested in applications of topology to physics and at mathematicians wishing to familiarize themselves with quantum field theory and the mathematical methods used in this field. It is accessible to graduate students in physics and mathematics.

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.

Conformal Field Theory and Topology

Author : Toshitake Kohno
Publisher : American Mathematical Soc.
ISBN 13 : 9780821821305
Total Pages : 188 pages
Book Rating : 4.8/5 (213 download)

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Book Synopsis Conformal Field Theory and Topology by : Toshitake Kohno

Download or read book Conformal Field Theory and Topology written by Toshitake Kohno and published by American Mathematical Soc.. This book was released on 2002 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry and physics have been developed with a strong influence on each other. One of the most remarkable interactions between geometry and physics since 1980 has been an application of quantum field theory to topology and differential geometry. This book focuses on a relationship between two-dimensional quantum field theory and three-dimensional topology which has been studied intensively since the discovery of the Jones polynomial in the middle of the 1980s and Witten's invariantfor 3-manifolds derived from Chern-Simons gauge theory. An essential difficulty in quantum field theory comes from infinite-dimensional freedom of a system. Techniques dealing with such infinite-dimensional objects developed in the framework of quantum field theory have been influential in geometryas well. This book gives an accessible treatment for a rigorous construction of topological invariants originally defined as partition functions of fields on manifolds. The book is organized as follows: The Introduction starts from classical mechanics and explains basic background materials in quantum field theory and geometry. Chapter 1 presents conformal field theory based on the geometry of loop groups. Chapter 2 deals with the holonomy of conformal field theory. Chapter 3 treatsChern-Simons perturbation theory. The final chapter discusses topological invariants for 3-manifolds derived from Chern-Simons perturbation theory.

Differential Topology and Quantum Field Theory

Author : Charles Nash
Publisher : Elsevier
ISBN 13 : 9780125140768
Total Pages : 404 pages
Book Rating : 4.1/5 (47 download)

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Book Synopsis Differential Topology and Quantum Field Theory by : Charles Nash

Download or read book Differential Topology and Quantum Field Theory written by Charles Nash and published by Elsevier. This book was released on 1991 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

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.

Topology, Geometry and Quantum Field Theory

Author : Ulrike Luise Tillmann
Publisher : Cambridge University Press
ISBN 13 : 9780521540490
Total Pages : 596 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Topology, Geometry and Quantum Field Theory by : Ulrike Luise Tillmann

Download or read book Topology, Geometry and Quantum Field Theory written by Ulrike Luise Tillmann and published by Cambridge University Press. This book was released on 2004-06-28 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Dirichlet Branes and Mirror Symmetry

Author : Paul Aspinwall
Publisher : American Mathematical Soc.
ISBN 13 : 0821838482
Total Pages : 698 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Dirichlet Branes and Mirror Symmetry by : Paul Aspinwall

Download or read book Dirichlet Branes and Mirror Symmetry written by Paul Aspinwall and published by American Mathematical Soc.. This book was released on 2009 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research in string theory has generated a rich interaction with algebraic geometry, with exciting work that includes the Strominger-Yau-Zaslow conjecture. This monograph builds on lectures at the 2002 Clay School on Geometry and String Theory that sought to bridge the gap between the languages of string theory and algebraic geometry.

Topological Quantum Field Theory and Four Manifolds

Author : Jose Labastida
Publisher : Springer Science & Business Media
ISBN 13 : 1402031777
Total Pages : 224 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Topological Quantum Field Theory and Four Manifolds by : Jose Labastida

Download or read book Topological Quantum Field Theory and Four Manifolds written by Jose Labastida and published by Springer Science & Business Media. This book was released on 2007-07-18 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: The emergence of topological quantum ?eld theory has been one of the most important breakthroughs which have occurred in the context of ma- ematical physics in the last century, a century characterizedbyindependent developments of the main ideas in both disciplines, physics and mathematics, which has concluded with two decades of strong interaction between them, where physics, as in previous centuries, has acted as a source of new mat- matics. Topological quantum ?eld theories constitute the core of these p- nomena, although the main drivingforce behind it has been the enormous e?ort made in theoretical particle physics to understand string theory as a theory able to unify the four fundamental interactions observed in nature. These theories set up a new realm where both disciplines pro?t from each other. Although the most striking results have appeared on the mathema- calside,theoreticalphysicshasclearlyalsobene?tted,sincethecorresponding developments have helped better to understand aspects of the fundamentals of ?eld and string theory.

Monoidal Categories and Topological Field Theory

Author : Vladimir Turaev
Publisher : Birkhäuser
ISBN 13 : 3319498347
Total Pages : 523 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Monoidal Categories and Topological Field Theory by : Vladimir Turaev

Download or read book Monoidal Categories and Topological Field Theory written by Vladimir Turaev and published by Birkhäuser. This book was released on 2017-06-28 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Frobenius Algebras and 2-D Topological Quantum Field Theories

Author : Joachim Kock
Publisher : Cambridge University Press
ISBN 13 : 9780521540315
Total Pages : 260 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Frobenius Algebras and 2-D Topological Quantum Field Theories by : Joachim Kock

Download or read book Frobenius Algebras and 2-D Topological Quantum Field Theories written by Joachim Kock and published by Cambridge University Press. This book was released on 2004 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2003 book describes a striking connection between topology and algebra, namely that 2D topological quantum field theories are equivalent to commutative Frobenius algebras. The precise formulation of the theorem and its proof is given in terms of monoidal categories, and the main purpose of the book is to develop these concepts from an elementary level, and more generally serve as an introduction to categorical viewpoints in mathematics. Rather than just proving the theorem, it is shown how the result fits into a more general pattern concerning universal monoidal categories for algebraic structures. Throughout, the emphasis is on the interplay between algebra and topology, with graphical interpretation of algebraic operations, and topological structures described algebraically in terms of generators and relations. The book will prove valuable to students or researchers entering this field who will learn a host of modern techniques that will prove useful for future work.

Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners

Author : Thomas Kerler
Publisher : Springer
ISBN 13 : 3540446257
Total Pages : 383 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners by : Thomas Kerler

Download or read book Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners written by Thomas Kerler and published by Springer. This book was released on 2003-07-01 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the (to date) most general approach to combinatorial constructions of topological quantum field theories (TQFTs) in three dimensions. The authors describe extended TQFTs as double functors between two naturally defined double categories: one of topological nature, made of 3-manifolds with corners, the other of algebraic nature, made of linear categories, functors, vector spaces and maps. Atiyah's conventional notion of TQFTs as well as the notion of modular functor from axiomatic conformal field theory are unified in this concept. A large class of such extended modular catergory is constructed, assigning a double functor to every abelian modular category, which does not have to be semisimple.

Quantum Topology

Author : Louis H. Kauffman
Publisher : World Scientific
ISBN 13 : 9789810225759
Total Pages : 400 pages
Book Rating : 4.2/5 (257 download)

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Book Synopsis Quantum Topology by : Louis H. Kauffman

Download or read book Quantum Topology written by Louis H. Kauffman and published by World Scientific. This book was released on 1993 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes a review volume on the relatively new subject of Quantum Topology. Quantum Topology has its inception in the 1984/1985 discoveries of new invariants of knots and links (Jones, Homfly and Kauffman polynomials). These invariants were rapidly connected with quantum groups and methods in statistical mechanics. This was followed by Edward Witten's introduction of methods of quantum field theory into the subject and the formulation by Witten and Michael Atiyah of the concept of topological quantum field theories.This book is a review volume of on-going research activity. The papers derive from talks given at the Special Session on Knot and Topological Quantum Field Theory of the American Mathematical Society held at Dayton, Ohio in the fall of 1992. The book consists of a self-contained article by Kauffman, entitled Introduction to Quantum Topology and eighteen research articles by participants in the special session.This book should provide a useful source of ideas and results for anyone interested in the interface between topology and quantum field theory.

The Universal Coefficient Theorem and Quantum Field Theory

Author : Andrei-Tudor Patrascu
Publisher : Springer
ISBN 13 : 3319461435
Total Pages : 270 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis The Universal Coefficient Theorem and Quantum Field Theory by : Andrei-Tudor Patrascu

Download or read book The Universal Coefficient Theorem and Quantum Field Theory written by Andrei-Tudor Patrascu and published by Springer. This book was released on 2016-09-23 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis describes a new connection between algebraic geometry, topology, number theory and quantum field theory. It offers a pedagogical introduction to algebraic topology, allowing readers to rapidly develop basic skills, and it also presents original ideas to inspire new research in the quest for dualities. Its ambitious goal is to construct a method based on the universal coefficient theorem for identifying new dualities connecting different domains of quantum field theory. This thesis opens a new area of research in the domain of non-perturbative physics—one in which the use of different coefficient structures in (co)homology may lead to previously unknown connections between different regimes of quantum field theories. The origin of dualities is an issue in fundamental physics that continues to puzzle the research community with unexpected results like the AdS/CFT duality or the ER-EPR conjecture. This thesis analyzes these observations from a novel and original point of view, mainly based on a fundamental connection between number theory and topology. Beyond its scientific qualities, it also offers a pedagogical introduction to advanced mathematics and its connection with physics. This makes it a valuable resource for students in mathematical physics and researchers wanting to gain insights into (co)homology theories with coefficients or the way in which Grothendieck's work may be connected with physics.

Geometry and Quantum Field Theory

Author : Daniel S. Freed
Publisher : American Mathematical Soc.
ISBN 13 : 9780821886830
Total Pages : 476 pages
Book Rating : 4.8/5 (868 download)

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Book Synopsis Geometry and Quantum Field Theory by : Daniel S. Freed

Download or read book Geometry and Quantum Field Theory written by Daniel S. Freed and published by American Mathematical Soc.. This book was released on 1995 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometry, Topology and Quantum Field Theory

Author : P. Bandyopadhyay
Publisher : Springer Science & Business Media
ISBN 13 : 9401716978
Total Pages : 225 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Geometry, Topology and Quantum Field Theory by : P. Bandyopadhyay

Download or read book Geometry, Topology and Quantum Field Theory written by P. Bandyopadhyay and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a monograph on geometrical and topological features which arise in quantum field theory. It is well known that when a chiral fermion interacts with a gauge field we have chiral anomaly which corresponds to the fact that divergence of the axial vector current does not vanish. It is observed that this is related to certain topological features associated with the fermion and leads to the realization of the topological origin of fermion number as well as the Berry phase. The role of gauge fields in the quantization procedure has its implications in these topological features of a fermion and helps us to consider a massive fermion as a soliton (skyrrnion). In this formalism chiral anomaly is found to be responsible for mass generation. This has its relevance in electroweak theory where it is observed that weak interaction gauge bosons attain mass topologically. The geometrical feature of a skyrmion also helps us to realize the internal symmetry of hadrons from reflection group. Finally it has been shown that noncommutative geometry where the space time manifold is taken to be X = M x Zz has its relevance in the description of a massive 4 fermion as a skyrmion when the discrete space is considered as the internal space and the symmetry breaking leads to chiral anomaly. In chap. l preliminary mathematical formulations related to the spinor structure have been discussed. In chap.

Topology and Quantum Theory in Interaction

Author : David Ayala
Publisher : American Mathematical Soc.
ISBN 13 : 1470442434
Total Pages : 258 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Topology and Quantum Theory in Interaction by : David Ayala

Download or read book Topology and Quantum Theory in Interaction written by David Ayala and published by American Mathematical Soc.. This book was released on 2018-10-25 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the NSF-CBMS Regional Conference on Topological and Geometric Methods in QFT, held from July 31–August 4, 2017, at Montana State University in Bozeman, Montana. In recent decades, there has been a movement to axiomatize quantum field theory into a mathematical structure. In a different direction, one can ask to test these axiom systems against physics. Can they be used to rederive known facts about quantum theories or, better yet, be the framework in which to solve open problems? Recently, Freed and Hopkins have provided a solution to a classification problem in condensed matter theory, which is ultimately based on the field theory axioms of Graeme Segal. Papers contained in this volume amplify various aspects of the Freed–Hopkins program, develop some category theory, which lies behind the cobordism hypothesis, the major structure theorem for topological field theories, and relate to Costello's approach to perturbative quantum field theory. Two papers on the latter use this framework to recover fundamental results about some physical theories: two-dimensional sigma-models and the bosonic string. Perhaps it is surprising that such sparse axiom systems encode enough structure to prove important results in physics. These successes can be taken as encouragement that the axiom systems are at least on the right track toward articulating what a quantum field theory is.

Quantum Field Theory of Many-Body Systems

Author : Xiao-Gang Wen
Publisher : OUP Oxford
ISBN 13 : 0191523968
Total Pages : 520 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Quantum Field Theory of Many-Body Systems by : Xiao-Gang Wen

Download or read book Quantum Field Theory of Many-Body Systems written by Xiao-Gang Wen and published by OUP Oxford. This book was released on 2004-06-04 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: For most of the last century, condensed matter physics has been dominated by band theory and Landau's symmetry breaking theory. In the last twenty years, however, there has been the emergence of a new paradigm associated with fractionalisation, topological order, emergent gauge bosons and fermions, and string condensation. These new physical concepts are so fundamental that they may even influence our understanding of the origin of light and fermions in the universe. This book is a pedagogical and systematic introduction to the new concepts and quantum field theoretical methods (which have fuelled the rapid developments) in condensed matter physics. It discusses many basic notions in theoretical physics which underlie physical phenomena in nature. Topics covered are dissipative quantum systems, boson condensation, symmetry breaking and gapless excitations, phase transitions, Fermi liquids, spin density wave states, Fermi and fractional statistics, quantum Hall effects, topological and quantum order, spin liquids, and string condensation. Methods covered are the path integral, Green's functions, mean-field theory, effective theory, renormalization group, bosonization in one- and higher dimensions, non-linear sigma-model, quantum gauge theory, dualities, slave-boson theory, and exactly soluble models beyond one-dimension. This book is aimed at teaching graduate students and bringing them to the frontiers of research in condensed matter physics.