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Proceedings Of The Geometric Algebraic And Topological Methods For Quantum Field Theory 2013
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Book Synopsis Geometric, Algebraic And Topological Methods For Quantum Field Theory - Proceedings Of The 2013 Villa De Leyva Summer School by : Alexander Cardona
Download or read book Geometric, Algebraic And Topological Methods For Quantum Field Theory - Proceedings Of The 2013 Villa De Leyva Summer School written by Alexander Cardona and published by World Scientific. This book was released on 2016-09-06 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Geometric, Algebraic and Topological Methods for Quantum Field Theory by : Sylvie Payche
Download or read book Geometric, Algebraic and Topological Methods for Quantum Field Theory written by Sylvie Payche and published by World Scientific. This book was released on 2014 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Geometric written by Leonardo Cano and published by . This book was released on 2016 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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."--Publisher's website.
Author :Alexander Cardona Publisher :World Scientific Publishing Company ISBN 13 :9789814730877 Total Pages :372 pages Book Rating :4.7/5 (38 download)
Book Synopsis Proceedings of the Geometric, Algebraic and Topological Methods for Quantum Field Theory 2013 by : Alexander Cardona
Download or read book Proceedings of the Geometric, Algebraic and Topological Methods for Quantum Field Theory 2013 written by Alexander Cardona and published by World Scientific Publishing Company. This book was released on 2016-02-28 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Quantization, Geometry and Noncommutative Structures in Mathematics and Physics by : Alexander Cardona
Download or read book Quantization, Geometry and Noncommutative Structures in Mathematics and Physics written by Alexander Cardona and published by Springer. This book was released on 2017-10-26 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents various ongoing approaches to the vast topic of quantization, which is the process of forming a quantum mechanical system starting from a classical one, and discusses their numerous fruitful interactions with mathematics.The opening chapter introduces the various forms of quantization and their interactions with each other and with mathematics.A first approach to quantization, called deformation quantization, consists of viewing the Planck constant as a small parameter. This approach provides a deformation of the structure of the algebra of classical observables rather than a radical change in the nature of the observables. When symmetries come into play, deformation quantization needs to be merged with group actions, which is presented in chapter 2, by Simone Gutt.The noncommutativity arising from quantization is the main concern of noncommutative geometry. Allowing for the presence of symmetries requires working with principal fiber bundles in a non-commutative setup, where Hopf algebras appear naturally. This is the topic of chapter 3, by Christian Kassel. Nichols algebras, a special type of Hopf algebras, are the subject of chapter 4, by Nicolás Andruskiewitsch. The purely algebraic approaches given in the previous chapters do not take the geometry of space-time into account. For this purpose a special treatment using a more geometric point of view is required. An approach to field quantization on curved space-time, with applications to cosmology, is presented in chapter 5 in an account of the lectures of Abhay Ashtekar that brings a complementary point of view to non-commutativity.An alternative quantization procedure is known under the name of string theory. In chapter 6 its supersymmetric version is presented. Superstrings have drawn the attention of many mathematicians, due to its various fruitful interactions with algebraic geometry, some of which are described here. The remaining chapters discuss further topics, as the Batalin-Vilkovisky formalism and direct products of spectral triples.This volume addresses both physicists and mathematicians and serves as an introduction to ongoing research in very active areas of mathematics and physics at the border line between geometry, topology, algebra and quantum field theory.
Book Synopsis Geometric and Topological Methods for Quantum Field Theory by : Alexander Cardona
Download or read book Geometric and Topological Methods for Quantum Field Theory written by Alexander Cardona and published by Cambridge University Press. This book was released on 2013-05-09 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Periods in Quantum Field Theory and Arithmetic by : José Ignacio Burgos Gil
Download or read book Periods in Quantum Field Theory and Arithmetic written by José Ignacio Burgos Gil and published by Springer Nature. This book was released on 2020-03-14 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the outcome of research initiatives formed during the special ``Research Trimester on Multiple Zeta Values, Multiple Polylogarithms, and Quantum Field Theory'' at the ICMAT (Instituto de Ciencias Matemáticas, Madrid) in 2014. The activity was aimed at understanding and deepening recent developments where Feynman and string amplitudes on the one hand, and periods and multiple zeta values on the other, have been at the heart of lively and fruitful interactions between theoretical physics and number theory over the past few decades. In this book, the reader will find research papers as well as survey articles, including open problems, on the interface between number theory, quantum field theory and string theory, written by leading experts in the respective fields. Topics include, among others, elliptic periods viewed from both a mathematical and a physical standpoint; further relations between periods and high energy physics, including cluster algebras and renormalisation theory; multiple Eisenstein series and q-analogues of multiple zeta values (also in connection with renormalisation); double shuffle and duality relations; alternative presentations of multiple zeta values using Ecalle's theory of moulds and arborification; a distribution formula for generalised complex and l-adic polylogarithms; Galois action on knots. Given its scope, the book offers a valuable resource for researchers and graduate students interested in topics related to both quantum field theory, in particular, scattering amplitudes, and number theory.
Book Synopsis Geometric And Topological Methods For Quantum Field Theory - Proceedings Of The Summer School by : Alexander Cardona
Download or read book Geometric And Topological Methods For Quantum Field Theory - Proceedings Of The Summer School written by Alexander Cardona and published by World Scientific. This book was released on 2003-03-21 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Partition Functions and Automorphic Forms by : Valery A. Gritsenko
Download or read book Partition Functions and Automorphic Forms written by Valery A. Gritsenko and published by Springer Nature. This book was released on 2020-07-09 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction to the research in several recently discovered and actively developing mathematical and mathematical physics areas. It focuses on: 1) Feynman integrals and modular functions, 2) hyperbolic and Lorentzian Kac-Moody algebras, related automorphic forms and applications to quantum gravity, 3) superconformal indices and elliptic hypergeometric integrals, related instanton partition functions, 4) moonshine, its arithmetic aspects, Jacobi forms, elliptic genus, and string theory, and 5) theory and applications of the elliptic Painleve equation, and aspects of Painleve equations in quantum field theories. All the topics covered are related to various partition functions emerging in different supersymmetric and ordinary quantum field theories in curved space-times of different (d=2,3,...,6) dimensions. Presenting multidisciplinary methods (localization, Borcherds products, theory of special functions, Cremona maps, etc) for treating a range of partition functions, the book is intended for graduate students and young postdocs interested in the interaction between quantum field theory and mathematics related to automorphic forms, representation theory, number theory and geometry, and mirror symmetry.
Book Synopsis Geometric, Algebraic And Topological Methods For Quantum Field Theory - Proceedings Of The 2011 Villa De Leyva Summer School by : Sylvie Paycha
Download or read book Geometric, Algebraic And Topological Methods For Quantum Field Theory - Proceedings Of The 2011 Villa De Leyva Summer School written by Sylvie Paycha and published by World Scientific. This book was released on 2013-11-15 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 202 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.
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.
Book Synopsis Proceedings of the Summer School Geometric and Topological Methods for Quantum Field Theory by : Hernan Ocampo
Download or read book Proceedings of the Summer School Geometric and Topological Methods for Quantum Field Theory written by Hernan Ocampo and published by World Scientific. This book was released on 2003 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Structural Aspects Of Quantum Field Theory And Noncommutative Geometry (Second Edition) (In 2 Volumes) by : Gerhard Grensing
Download or read book Structural Aspects Of Quantum Field Theory And Noncommutative Geometry (Second Edition) (In 2 Volumes) written by Gerhard Grensing and published by World Scientific. This book was released on 2021-07-15 with total page 1656 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Geometric and Topological Methods for Quantum Field Theory by : Alexander Cardona
Download or read book Geometric and Topological Methods for Quantum Field Theory written by Alexander Cardona and published by Cambridge University Press. This book was released on 2013-05-09 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique presentation of modern geometric methods in quantum field theory for researchers and graduate students in mathematics and physics.
Book Synopsis Nonperturbative Quantum Field Theory by : G. Hooft
Download or read book Nonperturbative Quantum Field Theory written by G. Hooft and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 603 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the past 15 years, quantum field theory and classical statistical mechanics have merged into a single field, and the need for nonperturbative methods for the description of critical phenomena in statistical mechanics as well as for problems in elementary particle physics are generally acknowledged. Such methods formed the central theme of the 1987 Cargese Advanced Study Institut. e on "Nonpert. urbat. ive Quantum Field Theory." The use of conformal symmet. ry has been of central interest in recent years, and was a main subject at. t. he ASI. Conformal invariant quantum field theory describes statistical mechanical systems exactly at a critical point, and can be analysed to a remarkable ext. ent. by group t. heoretical methods. Very strong results have been obtained for 2-dimensional systems. Conformal field theory is also the basis of string theory, which offers some hope of providing a unified t. heory of all interactions between elementary particles. Accordingly, a number of lectures and seminars were presented on these two topics. After syst. ematic introductory lectures, conformal field theory on Riemann surfaces, orbifolds, sigma models, and application of loop group theory and Grassmannians were discussed, and some ideas on modular geometry were presented. Other lectures combined' traditional techniques of constructive quant. um field theory with new methods such as the use of index-t. heorems and infinite dimensional (Kac Moody) symmetry groups. The problems encountered in a quantum mechanical description of black holes were discussed in detail.
Book Synopsis Quantum Field Theory for Economics and Finance by : B. E. Baaquie
Download or read book Quantum Field Theory for Economics and Finance written by B. E. Baaquie and published by Cambridge University Press. This book was released on 2018-08-23 with total page 717 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to how the mathematical tools from quantum field theory can be applied to economics and finance. Providing a range of quantum mathematical techniques for designing financial instruments, it demonstrates how a range of topics have quantum mechanical formulations, from asset pricing to interest rates.
