Non Semisimple Topological Quantum Field Theories For 3 Manifolds With Corners
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Author |
: Thomas Kerler |
Publisher |
: Springer |
Total Pages |
: 381 |
Release |
: 2003-07-01 |
ISBN-10 |
: 9783540446255 |
ISBN-13 |
: 3540446257 |
Rating |
: 4/5 (55 Downloads) |
Synopsis Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners by : Thomas Kerler
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 |
Publisher |
: |
Total Pages |
: 392 |
Release |
: 2014-09-01 |
ISBN-10 |
: 366219435X |
ISBN-13 |
: 9783662194355 |
Rating |
: 4/5 (5X Downloads) |
Synopsis Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners by : Thomas Kerler
Author |
: Marco De Renzi |
Publisher |
: American Mathematical Society |
Total Pages |
: 161 |
Release |
: 2022-05-24 |
ISBN-10 |
: 9781470452698 |
ISBN-13 |
: 1470452693 |
Rating |
: 4/5 (98 Downloads) |
Synopsis Non-Semisimple Extended Topological Quantum Field Theories by : Marco De Renzi
View the abstract.
Author |
: Jose Labastida |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 235 |
Release |
: 2007-07-18 |
ISBN-10 |
: 9781402031779 |
ISBN-13 |
: 1402031777 |
Rating |
: 4/5 (79 Downloads) |
Synopsis Topological Quantum Field Theory and Four Manifolds by : Jose Labastida
The emergence of topological quantum ?eld theory has been one of the most important breakthroughs which have occurred in the context of ma- ematical physics in the last century, a century characterizedbyindependent developments of the main ideas in both disciplines, physics and mathematics, which has concluded with two decades of strong interaction between them, where physics, as in previous centuries, has acted as a source of new mat- matics. Topological quantum ?eld theories constitute the core of these p- nomena, although the main drivingforce behind it has been the enormous e?ort made in theoretical particle physics to understand string theory as a theory able to unify the four fundamental interactions observed in nature. These theories set up a new realm where both disciplines pro?t from each other. Although the most striking results have appeared on the mathema- calside,theoreticalphysicshasclearlyalsobene?tted,sincethecorresponding developments have helped better to understand aspects of the fundamentals of ?eld and string theory.
Author |
: Marco De Renzi |
Publisher |
: |
Total Pages |
: 0 |
Release |
: 2022 |
ISBN-10 |
: 1470470969 |
ISBN-13 |
: 9781470470968 |
Rating |
: 4/5 (69 Downloads) |
Synopsis Non-semisimple Extended Topological Quantum Field Theories by : Marco De Renzi
"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 |
: Vijay Kodiyalam |
Publisher |
: CRC Press |
Total Pages |
: 138 |
Release |
: 2019-05-20 |
ISBN-10 |
: 142003555X |
ISBN-13 |
: 9781420035551 |
Rating |
: 4/5 (5X Downloads) |
Synopsis Topological Quantum Field Theories from Subfactors by : Vijay Kodiyalam
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 |
: Jin Ma |
Publisher |
: Springer |
Total Pages |
: 285 |
Release |
: 2007-04-24 |
ISBN-10 |
: 9783540488316 |
ISBN-13 |
: 3540488316 |
Rating |
: 4/5 (16 Downloads) |
Synopsis Forward-Backward Stochastic Differential Equations and their Applications by : Jin Ma
This volume is a survey/monograph on the recently developed theory of forward-backward stochastic differential equations (FBSDEs). Basic techniques such as the method of optimal control, the 'Four Step Scheme', and the method of continuation are presented in full. Related topics such as backward stochastic PDEs and many applications of FBSDEs are also discussed in detail. The volume is suitable for readers with basic knowledge of stochastic differential equations, and some exposure to the stochastic control theory and PDEs. It can be used for researchers and/or senior graduate students in the areas of probability, control theory, mathematical finance, and other related fields.
Author |
: Gershon Kresin |
Publisher |
: Springer |
Total Pages |
: 153 |
Release |
: 2007-03-05 |
ISBN-10 |
: 9783540695745 |
ISBN-13 |
: 3540695745 |
Rating |
: 4/5 (45 Downloads) |
Synopsis Sharp Real-Part Theorems by : Gershon Kresin
This volume contains a coherent point of view on various sharp pointwise inequalities for analytic functions in a disk in terms of the real part of the function on the boundary circle or in the disk itself. Inequalities of this type are frequently used in the theory of entire functions and in the analytic number theory.
Author |
: Ofer Gabber |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 324 |
Release |
: 2003 |
ISBN-10 |
: 3540405941 |
ISBN-13 |
: 9783540405948 |
Rating |
: 4/5 (41 Downloads) |
Synopsis Almost Ring Theory by : Ofer Gabber
Author |
: Horst Reinhard Beyer |
Publisher |
: Springer |
Total Pages |
: 291 |
Release |
: 2007-04-10 |
ISBN-10 |
: 9783540711292 |
ISBN-13 |
: 3540711295 |
Rating |
: 4/5 (92 Downloads) |
Synopsis Beyond Partial Differential Equations by : Horst Reinhard Beyer
This book introduces the treatment of linear and nonlinear (quasi-linear) abstract evolution equations by methods from the theory of strongly continuous semigroups. The theoretical part is accessible to graduate students with basic knowledge in functional analysis, with only some examples requiring more specialized knowledge from the spectral theory of linear, self-adjoint operators in Hilbert spaces. Emphasis is placed on equations of the hyperbolic type which are less often treated in the literature.