Quantum Topology and Global Anomalies PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Quantum Topology and Global Anomalies PDF full book. Access full book title Quantum Topology and Global Anomalies by R A Baadhio. Download full books in PDF and EPUB format.
Author: R A Baadhio Publisher: World Scientific ISBN: 9814498777 Category : Science Languages : en Pages : 284
Book Description
Anomalies are ubiquitous features in quantum field theories. They can ruin the consistency of such theories and put significant restrictions on their viability, especially in dimensions higher than four. Global gauge and gravitational anomalies are to date, one of the scant powerful and probing tools available to physicists in the pursuit of uniqueness. This monograph is one of the very few that specializes in the study of global anomalies in quantum field theories. A discussion of various issues associated to three dimensional physics — the Chern–Simons–Witten theories — widen the scope of this book. Topics discussed here comprises: the ongoing quest for three-manifolds invariant, the role of the mapping class groups in (a) the detection and cancellation of global anomalies, (b) formulating three-manifolds invariant; the geometric quantization of Chern-Simons-Witten theories; deformation quantization; study of chiral and gravitational anomalies; anomalies and the Atiyah-Patodi-Singer Index theorem; exotic spheres; global gravitational anomalies in some six and ten dimensional supergravity and superstring theories, with an additional case study of Witten SU(2) Global Gauge Anomalies. In addition, five chapters lay out the mathematical basis for a thorough use of the topics above. One chapter focuses on the relationship between Teichmüller spaces, moduli spaces and mapping class groups. Another chapter is devoted to mapping class groups and arithmetic groups. Gauge theories on Riemann surfaces are studies in well over two chapters, the first one centered on the theory of bundles and the second on connections. Many readers will find this a useful book, especially theoretical physicists and mathematicians. The material presented here will be of interest to both the experts who will find complete, detailed and precise descriptions of important topics of current interest in mathematical physics, and to students and newcomers to the field, who will appreciate the vast amount of information provided here, especially on global anomalies. Contents:The Ongoing Quest for Three-Manifold InvariantsMapping Class Groups and 3-Manifold InvariantsTeichmüller Spaces and Mapping Class GroupsMapping Class Groups and Arithmetic GroupsWeil-Petersson Geometry of Teichmüller SpacesGauge Theories on Riemann Surfaces I: BundlesGauge Theories on Riemann Surfaces II: ConnectionsGeometric Quantization of Chern–Simons–Witten TheoriesDeformation QuantizationChiral and Gravitational AnomaliesAnomalies and the Index TheoremGlobal AnomaliesMapping Class Groups and Global AnomaliesExotic Spheres Readership: Mathematicians and physicists. keywords:
Author: R A Baadhio Publisher: World Scientific ISBN: 9814498777 Category : Science Languages : en Pages : 284
Book Description
Anomalies are ubiquitous features in quantum field theories. They can ruin the consistency of such theories and put significant restrictions on their viability, especially in dimensions higher than four. Global gauge and gravitational anomalies are to date, one of the scant powerful and probing tools available to physicists in the pursuit of uniqueness. This monograph is one of the very few that specializes in the study of global anomalies in quantum field theories. A discussion of various issues associated to three dimensional physics — the Chern–Simons–Witten theories — widen the scope of this book. Topics discussed here comprises: the ongoing quest for three-manifolds invariant, the role of the mapping class groups in (a) the detection and cancellation of global anomalies, (b) formulating three-manifolds invariant; the geometric quantization of Chern-Simons-Witten theories; deformation quantization; study of chiral and gravitational anomalies; anomalies and the Atiyah-Patodi-Singer Index theorem; exotic spheres; global gravitational anomalies in some six and ten dimensional supergravity and superstring theories, with an additional case study of Witten SU(2) Global Gauge Anomalies. In addition, five chapters lay out the mathematical basis for a thorough use of the topics above. One chapter focuses on the relationship between Teichmüller spaces, moduli spaces and mapping class groups. Another chapter is devoted to mapping class groups and arithmetic groups. Gauge theories on Riemann surfaces are studies in well over two chapters, the first one centered on the theory of bundles and the second on connections. Many readers will find this a useful book, especially theoretical physicists and mathematicians. The material presented here will be of interest to both the experts who will find complete, detailed and precise descriptions of important topics of current interest in mathematical physics, and to students and newcomers to the field, who will appreciate the vast amount of information provided here, especially on global anomalies. Contents:The Ongoing Quest for Three-Manifold InvariantsMapping Class Groups and 3-Manifold InvariantsTeichmüller Spaces and Mapping Class GroupsMapping Class Groups and Arithmetic GroupsWeil-Petersson Geometry of Teichmüller SpacesGauge Theories on Riemann Surfaces I: BundlesGauge Theories on Riemann Surfaces II: ConnectionsGeometric Quantization of Chern–Simons–Witten TheoriesDeformation QuantizationChiral and Gravitational AnomaliesAnomalies and the Index TheoremGlobal AnomaliesMapping Class Groups and Global AnomaliesExotic Spheres Readership: Mathematicians and physicists. keywords:
Author: Randy A. Baadhio Publisher: World Scientific Publishing Company Incorporated ISBN: 9789810227272 Category : Gauge fields (Physics) Languages : en Pages : 270
Author: Louis H Kauffman Publisher: World Scientific ISBN: 9814502677 Category : Science Languages : en Pages : 392
Book Description
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. Contents:Introduction to Quantum Topology (L H Kauffman)Knot Theory, Exotic Spheres and Global Gravitational Anomalies (R A Baadhio)A Diagrammatic Theory of Knotted Surfaces (J S Carter & M Saito)A Categorical Construction of 4D Topological Quantum Field Theories (L Crane & D Yetter)Evaluating the Crane-Yetter Invariant (L Crane, L H Kauffman & D Yetter)A Method for Computing the Arf Invariants of Links (P Gilmer)Triangulations, Categories and Extended Topological Field Theories (R J Lawrence)The Casson Invariant for Two-Fold Branched Covers of Links (D Mullins)Elementary Conjectures in Classical Knot Theory (J H Przytycki)Knot Polynomials as States of Nonperturbative Four Dimensional Quantum Gravity (J Pullin)On Invariants of 3-Manifolds Derived from Abelian Groups (J Mattes, M M Polyak & N Reshetikhin)and other papers Readership: Mathematicians and mathematical physicists. keywords:Quantum Topology;Topological Quantum Field Theory;Meeting;AMS Special Session;Dayton, OH (USA)
Author: Reinhold A. Bertlmann Publisher: Oxford University Press ISBN: 9780198507628 Category : Science Languages : en Pages : 590
Book Description
This text presents the different aspects of the study of anomalies. Much emphasis is now being placed on the formulation of the theory using the mathematical ideas of differential geometry and topology. It includes derivations and calculations
Author: Louis H. Kauffman Publisher: World Scientific ISBN: 9789810225759 Category : Mathematics Languages : en Pages : 400
Book Description
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.
Author: Kazuo Fujikawa Publisher: OUP Oxford ISBN: 019152381X Category : Science Languages : en Pages : 297
Book Description
The Feynman path integrals are becoming increasingly important in the applications of quantum mechanics and field theory. The path integral formulation of quantum anomalies, i.e. the quantum breaking of certain symmetries, can now cover all the known quantum anomalies in a coherent manner. In this book the authors provide an introduction to the path integral method in quantum field theory and its applications to the analyses of quantum anomalies. No previous knowledge of field theory beyond advanced undergraduate quantum mechanics is assumed. The book provides the first coherent introductory treatment of the path integral formulation of chiral and Weyl anomalies, with applications to gauge theory in two and four dimensions, conformal field theory and string theory. Explicit and elementary path integral calculations of most of the quantum anomalies covered are given. The conceptual basis of the path integral bosonization in two-dimensional theory, which may have applications to condensed matter theory, for example, is clarified. The book also covers the recent interesting developments in the treatment of fermions and chiral anomalies in lattice gauge theory.
Author: Loriano Bonora Publisher: Springer Nature ISBN: 3031219287 Category : Science Languages : en Pages : 479
Book Description
This book presents a modern view of anomalies in quantum field theories. It is divided into six parts. The first part is preparatory covering an introduction to fermions, a description of the classical symmetries, and a short introduction to conformal symmetry. The second part of the book is devoted to the relation between anomalies and cohomology. The third part deals with perturbative methods to compute gauge, diffeomorphism and trace anomalies. In the fourth part the same anomalies are calculated with non-perturbative heat-kernel-like methods. Part five is devoted to the family's index theorem and its application to chiral anomalies, and to the differential characters and their applications to global anomalies. Part six is devoted to special topics including a complete calculation of trace and diffeomorphism anomalies of a Dirac fermion in a MAT background in two dimensions, Wess-Zumino terms in field theories, sigma models, their local and global anomalies and their cancelation, and finally the analysis of the worldsheet, sigma model, and target space anomalies of string and superstring theories. The book is targeted to researchers and graduate students.
Author: Daniel S. Freed Publisher: American Mathematical Soc. ISBN: 1470452065 Category : Algebraic topology Languages : en Pages : 186
Book Description
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.
Author: R A Baadhio
Author: R A Baadhio
Author: Randy A. Baadhio
Author: R A. Baddhio
Author: Louis H Kauffman
Author: Reinhold A. Bertlmann
Author: Louis H. Kauffman
Author: Kazuo Fujikawa
Author: Loriano Bonora
Author: William A. Bardeen
Author: Daniel S. Freed