Mathematical Aspects Of Conformal And Topological Field Theories And Quantum Groups
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Mathematical Aspects Of Conformal And Topological Field Theories And Quantum Groups
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Author : Paul J. Sally (Jr.)
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Mathematical Aspects Of Conformal And Topological Field Theories And Quantum Groups written by Paul J. Sally (Jr.) and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
This book contains papers presented by speakers at the AMS-IMS-SIAM Joint Summer Research Conference on Conformal Field Theory, Topological Field Theory and Quantum Groups, held at Mount Holyoke College in June 1992. One group of papers deals with one aspect of conformal field theory, namely, vertex operator algebras or superalgebras and their representations. Another group deals with various aspects of quantum groups. Other topics covered include the theory of knots in three-manifolds, symplectic geometry, and tensor products. This book provides an excellent view of some of the latest developments in this growing field of research.
Conformal Field Theories And Tensor Categories
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Author : Chengming Bai
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-30
Conformal Field Theories And Tensor Categories written by Chengming Bai and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-30 with Mathematics categories.
The present volume is a collection of seven papers that are either based on the talks presented at the workshop "Conformal field theories and tensor categories" held June 13 to June 17, 2011 at the Beijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researchers looking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.
Mathematical Aspects Of Quantum Field Theories
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Author : Damien Calaque
language : en
Publisher: Springer
Release Date : 2015-01-06
Mathematical Aspects Of Quantum Field Theories written by Damien Calaque and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-06 with Science categories.
Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homology and factorization algebras.
Lectures On Field Theory And Topology
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Author : Daniel S. Freed
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-08-23
Lectures On Field Theory And Topology written by Daniel S. Freed and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-23 with Mathematics categories.
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.
Harmonic Analysis And Nonlinear Differential Equations
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Author : Victor Lenard Shapiro
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Harmonic Analysis And Nonlinear Differential Equations written by Victor Lenard Shapiro and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
There are also several survey articles on recent developments in multiple trigonometric series, dyadic harmonic analysis, special functions, analysis on fractals, and shock waves, as well as papers with new results in nonlinear differential equations. These survey articles, along with several of the research articles, cover a wide variety of applications such as turbulence, general relativity and black holes, neural networks, and diffusion and wave propagation in porous media.
Representations Of Algebraic Groups
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Author : Jens Carsten Jantzen
language : en
Publisher: American Mathematical Soc.
Release Date : 2003-01-01
Representations Of Algebraic Groups written by Jens Carsten Jantzen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.
Now back in print by the AMS, this is a significantly revised edition of a book originally published in 1987 by Academic Press. This book gives the reader an introduction to the theory of algebraic representations of reductive algebraic groups. To develop appropriate techniques, the first part of the book is an introduction to the general theory of representations of algebraic group schemes. Here, the author describes important basic notions: induction functors, cohomology,quotients, Frobenius kernels, and reduction mod $p$, among others. The second part of the book is devoted to the representation theory of reductive algebraic groups. It includes topics such as the description of simple modules, vanishing theorems, the Borel-Bott-Weil theorem and Weyl's character formula, andSchubert schemes and line bundles on them. For this revised edition the author added nearly 150 pages of new material describing some later developments, among them Schur algebras, Lusztig's conjecture and Kazhdan-Lusztig polynomials, tilting modules, and representations of quantum groups. He also made major revisions to parts of the old text. Jantzen's book continues to be the ultimate source of information on representations of algebraic groups in finite characteristics. It is suitable forgraduate students and research mathematicians interested in algebraic groups and their representations.
Interactions Of Quantum Affine Algebras With Cluster Algebras Current Algebras And Categorification
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Author : Jacob Greenstein
language : en
Publisher: Springer Nature
Release Date : 2022-03-11
Interactions Of Quantum Affine Algebras With Cluster Algebras Current Algebras And Categorification written by Jacob Greenstein and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-11 with Mathematics categories.
This volume collects chapters that examine representation theory as connected with affine Lie algebras and their quantum analogues, in celebration of the impact Vyjayanthi Chari has had on this area. The opening chapters are based on mini-courses given at the conference “Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification”, held on the occasion of Chari’s 60th birthday at the Catholic University of America in Washington D.C., June 2018. The chapters that follow present a broad view of the area, featuring surveys, original research, and an overview of Vyjayanthi Chari’s significant contributions. Written by distinguished experts in representation theory, a range of topics are covered, including: String diagrams and categorification Quantum affine algebras and cluster algebras Steinberg groups for Jordan pairs Dynamical quantum determinants and Pfaffians Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification will be an ideal resource for researchers in the fields of representation theory and mathematical physics.
The Feynman Integral And Feynman S Operational Calculus
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Author : Gerald W. Johnson
language : en
Publisher: Clarendon Press
Release Date : 2000-03-16
The Feynman Integral And Feynman S Operational Calculus written by Gerald W. Johnson and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-03-16 with Mathematics categories.
This book provides the most comprehensive mathematical treatment to date of the Feynman path integral and Feynman's operational calculus. It is accessible to mathematicians, mathematical physicists and theoretical physicists. Including new results and much material previously only available in the research literature, this book discusses both the mathematics and physics background that motivate the study of the Feynman path integral and Feynman's operational calculus, and also provides more detailed proofs of the central results.
Set Theory
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Author : Tomek Bartoszyński
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Set Theory written by Tomek Bartoszyński and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
This book consists of papers presented at the first three meetings of the Boise Extravaganza in Set Theory (BEST) at Boise State University, Idaho, in 1992, 1993, and 1994. Articles in this volume present recent results in several areas of set theory.
Groups Algebras And Applications
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Author : César Polcino Milies
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Groups Algebras And Applications written by César Polcino Milies and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
Contains the proceedings of the XVIII Latin American Algebra Colloquium, held from August 3-8, 2009, in Sao Paulo, Brazil. It includes research articles as well as up-to-date surveys covering several directions of current research in algebra, such as Asymptotic Codimension Growth, Hopf Algebras, Structure Theory of both Associative and Non-Associative Algebras, Partial Actions of Groups on Rings, and contributions to Coding Theory.