Topological Methods In Quantum Field Theories PDF Download
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| Author | : Hernan Ocampo |
| Publisher | : Cambridge University Press |
| Total Pages | : 435 |
| Release | : 2010-04-29 |
| Genre | : Science |
| ISBN | : 113948673X |
Download Geometric and Topological Methods for Quantum Field Theory Book in PDF, ePub and Kindle
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 | : Albert S. Schwarz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 277 |
| Release | : 2013-04-09 |
| Genre | : Mathematics |
| ISBN | : 366202943X |
Download Quantum Field Theory and Topology Book in PDF, ePub and Kindle
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.
| Author | : Werner Nahm |
| Publisher | : World Scientific |
| Total Pages | : 184 |
| Release | : 1991-05-17 |
| Genre | : |
| ISBN | : 9814569429 |
Download Topological Methods In Quantum Field Theories Book in PDF, ePub and Kindle
Over the last two decades, topological ideas have found increasingly more applications in quantum field theory. Topological field theories are the culmination of these developments, and they formed the dominating theme of the conference. The other focal point was two-dimensional quantum gravity. The participation of such leading mathematicians as M Atiyah, R Bott, G Segal, and I Singer, is a testmony to the deep interplay of mathematics and theoretical physics.
| Author | : Alexander Cardona |
| Publisher | : World Scientific |
| Total Pages | : 495 |
| Release | : 2003-03-21 |
| Genre | : Mathematics |
| ISBN | : 9814487678 |
Download Geometric And Topological Methods For Quantum Field Theory - Proceedings Of The Summer School Book in PDF, ePub and Kindle
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 | : Alexander Cardona |
| Publisher | : World Scientific |
| Total Pages | : 385 |
| Release | : 2016-09-06 |
| Genre | : Mathematics |
| ISBN | : 9814730890 |
Download Geometric, Algebraic And Topological Methods For Quantum Field Theory - Proceedings Of The 2013 Villa De Leyva Summer School Book in PDF, ePub and Kindle
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 | : Sylvie Payche |
| Publisher | : World Scientific |
| Total Pages | : 378 |
| Release | : 2014 |
| Genre | : Science |
| ISBN | : 9814460052 |
Download Geometric, Algebraic and Topological Methods for Quantum Field Theory Book in PDF, ePub and Kindle
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 | : Hernan Ocampo |
| Publisher | : World Scientific |
| Total Pages | : 495 |
| Release | : 2003 |
| Genre | : Science |
| ISBN | : 9812381317 |
Download Proceedings of the Summer School Geometric and Topological Methods for Quantum Field Theory Book in PDF, ePub and Kindle
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 | : G. Giachetta |
| Publisher | : World Scientific |
| Total Pages | : 715 |
| Release | : 2005 |
| Genre | : Science |
| ISBN | : 9812701265 |
Download Geometric and Algebraic Topological Methods in Quantum Mechanics Book in PDF, ePub and Kindle
In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry''s geometric factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques based on the deep interplay between algebra, differential geometry and topology. The book aims at being a guide to advanced differential geometric and topological methods in quantum mechanics. Their main peculiarity lies in the fact that geometry in quantum theory speaks mainly the algebraic language of rings, modules, sheaves and categories. Geometry is by no means the primary scope of the book, but it underlies many ideas in modern quantum physics and provides the most advanced schemes of quantization.
| Author | : Charles Nash |
| Publisher | : Elsevier |
| Total Pages | : 404 |
| Release | : 1991 |
| Genre | : Mathematics |
| ISBN | : 9780125140768 |
Download Differential Topology and Quantum Field Theory Book in PDF, ePub and Kindle
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
| Author | : Toshitake Kohno |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 188 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 9780821821305 |
Download Conformal Field Theory and Topology Book in PDF, ePub and Kindle
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.
