Conformal Field Theory Automorphic Forms And Related Topics

Author : Winfried Kohnen,Rainer Weissauer
Publisher : Springer
Page : 370 pages
File Size : 48,5 Mb
Release : 2014-08-22
Category : Mathematics
ISBN : 9783662438312

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Conformal Field Theory, Automorphic Forms and Related Topics by Winfried Kohnen,Rainer Weissauer Pdf

This book, part of the series Contributions in Mathematical and Computational Sciences, reviews recent developments in the theory of vertex operator algebras (VOAs) and their applications to mathematics and physics. The mathematical theory of VOAs originated from the famous monstrous moonshine conjectures of J.H. Conway and S.P. Norton, which predicted a deep relationship between the characters of the largest simple finite sporadic group, the Monster and the theory of modular forms inspired by the observations of J. MacKay and J. Thompson. The contributions are based on lectures delivered at the 2011 conference on Conformal Field Theory, Automorphic Forms and Related Topics, organized by the editors as part of a special program offered at Heidelberg University that summer under the sponsorship of the Mathematics Center Heidelberg (MATCH).

Author : Valery A. Gritsenko,Vyacheslav P. Spiridonov
Publisher : Springer Nature
Page : 422 pages
File Size : 50,9 Mb
Release : 2020-07-09
Category : Mathematics
ISBN : 9783030424008

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Partition Functions and Automorphic Forms by Valery A. Gritsenko,Vyacheslav P. Spiridonov Pdf

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.

Author : Matthew Krauel,Michael Tuite,Gaywalee Yamskulna
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 49,7 Mb
Release : 2020-07-13
Category : Education
ISBN : 9781470449384

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Vertex Operator Algebras, Number Theory and Related Topics by Matthew Krauel,Michael Tuite,Gaywalee Yamskulna Pdf

This volume contains the proceedings of the International Conference on Vertex Operator Algebras, Number Theory, and Related Topics, held from June 11–15, 2018, at California State University, Sacramento, California. The mathematics of vertex operator algebras, vector-valued modular forms and finite group theory continues to provide a rich and vibrant landscape in mathematics and physics. The resurgence of moonshine related to the Mathieu group and other groups, the increasing role of algebraic geometry and the development of irrational vertex operator algebras are just a few of the exciting and active areas at present. The proceedings center around active research on vertex operator algebras and vector-valued modular forms and offer original contributions to the areas of vertex algebras and number theory, surveys on some of the most important topics relevant to these fields, introductions to new fields related to these and open problems from some of the leaders in these areas.

Author : Kenji Ueno
Publisher : American Mathematical Soc.
Page : 178 pages
File Size : 46,9 Mb
Release : 2008
Category : Conformal invariants
ISBN : 9780821840887

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Conformal Field Theory with Gauge Symmetry by Kenji Ueno Pdf

This book presents a systematic approach to conformal field theory with gauge symmetry from the point of view of complex algebraic geometry. After presenting the basic facts of the theory of compact Riemann surfaces and the representation theory of affine Lie algebras in Chapters 1 and 2, conformal blocks for pointed Riemann surfaces with coordinates are constructed in Chapter 3. In Chapter 4 the sheaf of conformal blocks associated to a family of pointed Riemann surfaces withcoordinates is constructed, and in Chapter 5 it is shown that this sheaf supports a projective flat connection-one of the most important facts of conformal field theory. Chapter 6 is devoted to the study of the detailed structure of the conformal field theory over $\mathbb{P}1$.Recently it was shown that modular functors can be constructed from conformal field theory, giving an interesting relationship between algebraic geometry and topological quantum field theory. This book provides a timely introduction to an intensively studied topic of conformal field theory with gauge symmetry by a leading algebraic geometer, and includes all the necessary techniques and results that are used to construct the modular functor.

Author : Sandra Pinelas,Tomás Caraballo,Peter Kloeden,John R. Graef
Publisher : Springer
Page : 662 pages
File Size : 40,7 Mb
Release : 2018-05-08
Category : Mathematics
ISBN : 9783319756479

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Differential and Difference Equations with Applications by Sandra Pinelas,Tomás Caraballo,Peter Kloeden,John R. Graef Pdf

This book gathers papers from the International Conference on Differential & Difference Equations and Applications 2017 (ICDDEA 2017), held in Lisbon, Portugal on June 5-9, 2017. The editors have compiled the strongest research presented at the conference, providing readers with valuable insights into new trends in the field, as well as applications and high-level survey results. The goal of the ICDDEA was to promote fruitful collaborations between researchers in the fields of differential and difference equations. All areas of differential and difference equations are represented, with a special emphasis on applications.

Author : Martin Schottenloher
Publisher : Springer Science & Business Media
Page : 153 pages
File Size : 43,8 Mb
Release : 2008-09-15
Category : Science
ISBN : 9783540706908

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A Mathematical Introduction to Conformal Field Theory by Martin Schottenloher Pdf

Part I gives a detailed, self-contained and mathematically rigorous exposition of classical conformal symmetry in n dimensions and its quantization in two dimensions. The conformal groups are determined and the appearence of the Virasoro algebra in the context of the quantization of two-dimensional conformal symmetry is explained via the classification of central extensions of Lie algebras and groups. Part II surveys more advanced topics of conformal field theory such as the representation theory of the Virasoro algebra, conformal symmetry within string theory, an axiomatic approach to Euclidean conformally covariant quantum field theory and a mathematical interpretation of the Verlinde formula in the context of moduli spaces of holomorphic vector bundles on a Riemann surface.

Author : Dražen Adamović,Andrej Dujella,Antun Milas,Pavle Pandžić
Publisher : American Mathematical Soc.
Page : 122 pages
File Size : 48,7 Mb
Release : 2021-05-10
Category : Education
ISBN : 9781470453510

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Lie Groups, Number Theory, and Vertex Algebras by Dražen Adamović,Andrej Dujella,Antun Milas,Pavle Pandžić Pdf

This volume contains the proceedings of the conference Representation Theory XVI, held from June 25–29, 2019, in Dubrovnik, Croatia. The articles in the volume address selected aspects of representation theory of reductive Lie groups and vertex algebras, and are written by prominent experts in the field as well as junior researchers. The three main topics of these articles are Lie theory, number theory, and vertex algebras.

Author : M Jimbo
Publisher : Elsevier
Page : 439 pages
File Size : 43,7 Mb
Release : 2012-12-02
Category : Science
ISBN : 9780323150354

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Conformal Field Theory and Solvable Lattice Models by M Jimbo Pdf

Advanced Studies in Pure Mathematics, 16: Conformal Field Theory and Solvable Lattice Models contains nine papers based on the symposium "Conformal field theory and solvable lattice models" held at RIMS, Kyoto, May 1986. These papers cover the following active areas in mathematical physics: conformal field theory, solvable lattice models, affine and Virasoro algebra, and KP equations. The volume begins with an analysis of 1 and 2 point correlation functions of the Gibbs measure of random matrices. This is followed by separate chapters on solvable solid-on-solid (SOS) models; lectures on conformal field theory; the construction of Fermion variables for the 3D Ising Model; and vertex operator construction of null fields (singular vertex operators) based on the oscillator representation of conformal and superconformal algebras with central charge extention. Subsequent chapters deal with Hecke algebra representations of braid groups and classical Yang-Baxter equations; the relationship between the conformal field theories and the soliton equations (KdV, MKdV and Sine-Gordon, etc.) at both quantum and classical levels; and a supersymmetric extension of the Kadomtsev-Petviashvili hierarchy.

Author : Thomas Creutzig,Shashank Kanade,Robert McRae
Publisher : American Mathematical Society
Page : 194 pages
File Size : 47,5 Mb
Release : 2024-04-17
Category : Mathematics
ISBN : 9781470467241

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Tensor Categories for Vertex Operator Superalgebra Extensions by Thomas Creutzig,Shashank Kanade,Robert McRae Pdf

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Author : Chengming Bai,Jürgen Fuchs,Yi-Zhi Huang,Liang Kong,Ingo Runkel,Christoph Schweigert
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 53,8 Mb
Release : 2013-10-30
Category : Mathematics
ISBN : 9783642393839

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Conformal Field Theories and Tensor Categories by Chengming Bai,Jürgen Fuchs,Yi-Zhi Huang,Liang Kong,Ingo Runkel,Christoph Schweigert Pdf

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.

Author : Katrina Barron,Elizabeth Jurisich,Antun Milas,Kailash Misr
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 49,6 Mb
Release : 2017-08-15
Category : Lie algebras
ISBN : 9781470426668

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Lie Algebras, Vertex Operator Algebras, and Related Topics by Katrina Barron,Elizabeth Jurisich,Antun Milas,Kailash Misr Pdf

This volume contains the proceedings of the conference on Lie Algebras, Vertex Operator Algebras, and Related Topics, celebrating the 70th birthday of James Lepowsky and Robert Wilson, held from August 14–18, 2015, at the University of Notre Dame, Notre Dame, Indiana. Since their seminal work in the 1970s, Lepowsky and Wilson, their collaborators, their students, and those inspired by their work, have developed an amazing body of work intertwining the fields of Lie algebras, vertex algebras, number theory, theoretical physics, quantum groups, the representation theory of finite simple groups, and more. The papers presented here include recent results and descriptions of ongoing research initiatives representing the broad influence and deep connections brought about by the work of Lepowsky and Wilson and include a contribution by Yi-Zhi Huang summarizing some major open problems in these areas, in particular as they pertain to two-dimensional conformal field theory.

Author : Martin Schottenloher
Publisher : Springer Science & Business Media
Page : 254 pages
File Size : 40,5 Mb
Release : 2008-09-26
Category : Science
ISBN : 9783540686255

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A Mathematical Introduction to Conformal Field Theory by Martin Schottenloher Pdf

The first part of this book gives a self-contained and mathematically rigorous exposition of classical conformal symmetry in n dimensions and its quantization in two dimensions. The second part surveys some more advanced topics of conformal field theory.

Author : R. Mirman
Publisher : iUniverse
Page : 313 pages
File Size : 42,6 Mb
Release : 2005-02
Category : Science
ISBN : 9780595336920

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Quantum Field Theory Conformal Group Theory Conformal Field Theory by R. Mirman Pdf

The conformal group is the invariance group of geometry (which is not understood), the largest one. Physical applications are implied, as discussed, including reasons for interactions. The group structure as well as those of related groups are analyzed. An inhomogeneous group is a subgroup of a homogeneous one because of nonlinearities of the realization. Conservation of baryons (protons can't decay) is explained and proven. Reasons for various realizations, so matrix elements, of the Lorentz group given. The clearly relevant mass level formula is compared with experimental values. Questions, implications and possibilities, including for differential equations, are raised.

Author : Kishore Marathe
Publisher : Springer Science & Business Media
Page : 458 pages
File Size : 41,5 Mb
Release : 2010-08-09
Category : Mathematics
ISBN : 9781848829398

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Topics in Physical Mathematics by Kishore Marathe Pdf

As many readers will know, the 20th century was a time when the fields of mathematics and the sciences were seen as two separate entities. Caused by the rapid growth of the physical sciences and an increasing abstraction in mathematical research, each party, physicists and mathematicians alike, suffered a misconception; not only of the opposition’s theoretical underpinning, but of how the two subjects could be intertwined and effectively utilized. One sub-discipline that played a part in the union of the two subjects is Theoretical Physics. Breaking it down further came the fundamental theories, Relativity and Quantum theory, and later on Yang-Mills theory. Other areas to emerge in this area are those derived from the works of Donaldson, Chern-Simons, Floer-Fukaya, and Seiberg-Witten. Aimed at a wide audience, Physical Topics in Mathematics demonstrates how various physical theories have played a crucial role in the developments of Mathematics and in particular, Geometric Topology. Issues are studied in great detail, and the book steadfastly covers the background of both Mathematics and Theoretical Physics in an effort to bring the reader to a deeper understanding of their interaction. Whilst the world of Theoretical Physics and Mathematics is boundless; it is not the intention of this book to cover its enormity. Instead, it seeks to lead the reader through the world of Physical Mathematics; leaving them with a choice of which realm they wish to visit next.

Author : Mamoru Mimura
Publisher : Springer
Page : 246 pages
File Size : 41,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540469384

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Homotopy Theory and Related Topics by Mamoru Mimura Pdf