Non Semisimple Extended Topological Quantum Field Theories

Author : Marco De Renzi
Publisher : Unknown
Page : 0 pages
File Size : 43,6 Mb
Release : 2022
Category : Electronic books
ISBN : 1470470969

Get Book

Non-semisimple Extended Topological Quantum Field Theories by Marco De Renzi Pdf

"We develop the general theory for the construction of Extended Topological Quantum Field Theories (ETQFTs) associated with the Costantino-Geer-Patureau quantum invariants of closed 3-manifolds. In order to do so, we introduce relative modular categories, a class of ribbon categories which are modeled on representations of unrolled quantum groups, and which can be thought of as a non-semisimple analogue to modular categories. Our approach exploits a 2-categorical version of the universal construction introduced by Blanchet, Habegger, Masbaum, and Vogel. The 1+1+1-EQFTs thus obtained are realized by symmetric monoidal 2-functors which are defined over non-rigid 2-categories of admissible cobordisms decorated with colored ribbon graphs and cohomology classes, and which take values in 2- categories of complete graded linear categories. In particular, our construction extends the family of graded 2+1-TQFTs defined for the unrolled version of quantum sl2 by Blanchet, Costantino, Geer, and Patureau to a new family of graded ETQFTs. The non-semisimplicity of the theory is witnessed by the presence of non-semisimple graded linear categories associated with critical 1-manifolds"--

Author : Thomas Kerler,Volodymyr V. Lyubashenko
Publisher : Springer
Page : 381 pages
File Size : 53,5 Mb
Release : 2003-07-01
Category : Mathematics
ISBN : 9783540446255

Get Book

Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners by Thomas Kerler,Volodymyr V. Lyubashenko Pdf

This book presents the (to date) most general approach to combinatorial constructions of topological quantum field theories (TQFTs) in three dimensions. The authors describe extended TQFTs as double functors between two naturally defined double categories: one of topological nature, made of 3-manifolds with corners, the other of algebraic nature, made of linear categories, functors, vector spaces and maps. Atiyah's conventional notion of TQFTs as well as the notion of modular functor from axiomatic conformal field theory are unified in this concept. A large class of such extended modular catergory is constructed, assigning a double functor to every abelian modular category, which does not have to be semisimple.

Author : Thomas Kerler,Volodymyr V. Lyubashenko
Publisher : Unknown
Page : 392 pages
File Size : 44,8 Mb
Release : 2014-09-01
Category : Electronic
ISBN : 366219435X

Get Book

Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners by Thomas Kerler,Volodymyr V. Lyubashenko Pdf

Author : Marco De Renzi
Publisher : American Mathematical Society
Page : 161 pages
File Size : 43,9 Mb
Release : 2022-05-24
Category : Mathematics
ISBN : 9781470452698

Get Book

Non-Semisimple Extended Topological Quantum Field Theories by Marco De Renzi Pdf

View the abstract.

Author : Vladimir G. Turaev
Publisher : Walter de Gruyter GmbH & Co KG
Page : 600 pages
File Size : 49,7 Mb
Release : 2020-03-23
Category : Mathematics
ISBN : 9783110883275

Get Book

Quantum Invariants of Knots and 3-Manifolds by Vladimir G. Turaev Pdf

This monograph provides a systematic treatment of topological quantum field theories (TQFT's) in three dimensions, inspired by the discovery of the Jones polynomial of knots, the Witten-Chern-Simons field theory, and the theory of quantum groups. The author, one of the leading experts in the subject, gives a rigorous and self-contained exposition of new fundamental algebraic and topological concepts that emerged in this theory. The book is divided into three parts. Part I presents a construction of 3-dimensional TQFT's and 2-dimensional modular functors from so-called modular categories. This gives new knot and 3-manifold invariants as well as linear representations of the mapping class groups of surfaces. In Part II the machinery of 6j-symbols is used to define state sum invariants of 3-manifolds. Their relation to the TQFT's constructed in Part I is established via the theory of shadows. Part III provides constructions of modular categories, based on quantum groups and Kauffman's skein modules. This book is accessible to graduate students in mathematics and physics with a knowledge of basic algebra and topology. It will be an indispensable source for everyone who wishes to enter the forefront of this rapidly growing and fascinating area at the borderline of mathematics and physics. Most of the results and techniques presented here appear in book form for the first time.

Author : Vijay Kodiyalam
Publisher : CRC Press
Page : 138 pages
File Size : 51,9 Mb
Release : 2019-05-20
Category : Mathematics
ISBN : 142003555X

Get Book

Topological Quantum Field Theories from Subfactors by Vijay Kodiyalam Pdf

Pure mathematicians have only recently begun a rigorous study of topological quantum field theories (TQFTs). Ocneanu, in particular, showed that subfactors yield TQFTs that complement the Turaev-Viro construction. Until now, however, it has been difficult to find an account of this work that is both detailed and accessible. Topological Quant

Author : Jenny Fuselier,Ling Long,Ravi Ramakrishna,Holly Swisher,Fang-Ting Tu
Publisher : American Mathematical Society
Page : 138 pages
File Size : 46,9 Mb
Release : 2022-11-10
Category : Mathematics
ISBN : 9781470454333

Get Book

Hypergeometric Functions Over Finite Fields by Jenny Fuselier,Ling Long,Ravi Ramakrishna,Holly Swisher,Fang-Ting Tu Pdf

View the abstract.

Author : André Gil Henriques,David Penneys,James E. Tener
Publisher : American Mathematical Society
Page : 100 pages
File Size : 53,8 Mb
Release : 2023-02-13
Category : Mathematics
ISBN : 9781470455408

Get Book

Planar Algebras in Braided Tensor Categories by André Gil Henriques,David Penneys,James E. Tener Pdf

View the abstract.

Author : John M. Bryden
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 49,7 Mb
Release : 2005-03-02
Category : Mathematics
ISBN : 9781402027703

Get Book

Advances in Topological Quantum Field Theory by John M. Bryden Pdf

Author : Chris Kottke,Michael Singer
Publisher : American Mathematical Society
Page : 124 pages
File Size : 49,9 Mb
Release : 2022-11-10
Category : Mathematics
ISBN : 9781470455415

Get Book

Partial Compactification of Monopoles and Metric Asymptotics by Chris Kottke,Michael Singer Pdf

View the abstract.

Author : Michael Hitrik,Andrea Mantile,Johannes Sjöstrand
Publisher : American Mathematical Society
Page : 102 pages
File Size : 49,8 Mb
Release : 2022-11-10
Category : Mathematics
ISBN : 9781470454210

Get Book

Adiabatic Evolution and Shape Resonances by Michael Hitrik,Andrea Mantile,Johannes Sjöstrand Pdf

View the abstract.

Author : M. J. Bergvelt,Gaywalee Yamskulna,Wenhua Zhao
Publisher : American Mathematical Soc.
Page : 246 pages
File Size : 47,9 Mb
Release : 2009-10-01
Category : Mathematics
ISBN : 9780821848401

Get Book

Vertex Operator Algebras and Related Areas by M. J. Bergvelt,Gaywalee Yamskulna,Wenhua Zhao Pdf

Vertex operator algebras were introduced to mathematics in the work of Richard Borcherds, Igor Frenkel, James Lepowsky and Arne Meurman as a mathematically rigorous formulation of chiral algebras of two-dimensional conformal field theory. The aim was to use vertex operator algebras to explain and prove the remarkable Monstrous Moonshine conjectures in group theory. The theory of vertex operator algebras has now grown into a major research area in mathematics. These proceedings contain expository lectures and research papers presented during the international conference on Vertex Operator Algebras and Related Areas, held at Illinois State University in Normal, IL, from July 7 to July 11, 2008. The main aspects of this conference were connections and interactions of vertex operator algebras with the following areas: conformal field theories, quantum field theories, Hopf algebra, infinite dimensional Lie algebras, and modular forms. This book will be useful for researchers as well as for graduate students in mathematics and physics. Its purpose is not only to give an up-to-date overview of the fields covered by the conference but also to stimulate new directions and discoveries by experts in the areas.

Author : Lucia Di Vizio,Charlotte Hardouin
Publisher : American Mathematical Society
Page : 88 pages
File Size : 52,9 Mb
Release : 2022-08-31
Category : Mathematics
ISBN : 9781470453848

Get Book

Intrinsic Approach to Galois Theory of $q$-Difference Equations by Lucia Di Vizio,Charlotte Hardouin Pdf

View the abstract.

Author : Christopher John Schommer-Pries
Publisher : Unknown
Page : 540 pages
File Size : 45,9 Mb
Release : 2009
Category : Electronic
ISBN : UCAL:C3522734

Get Book

The Classification of Two-dimensional Extended Topological Field Theories by Christopher John Schommer-Pries Pdf

Author : Zhaobing Fan,Chun-Ju Lai,Yiqiang Li,Li Luo,Weiqiang Wang
Publisher : American Mathematical Society
Page : 108 pages
File Size : 45,5 Mb
Release : 2023-01-18
Category : Mathematics
ISBN : 9781470456269

Get Book

Affine Hecke Algebras and Quantum Symmetric Pairs by Zhaobing Fan,Chun-Ju Lai,Yiqiang Li,Li Luo,Weiqiang Wang Pdf

View the abstract.