Combinatorial quantization of the Hamiltonian Chern-Simons theory I
TLDR
In this article, the authors describe a mathematically precise quantization of the Hamiltonian Chern-Simons theory on the lattice which is expected to reproduce the results of the continuous theory exactly.Abstract:
Motivated by a recent paper of Fock and Rosly [6] we describe a mathematically precise quantization of the Hamiltonian Chern-Simons theory. We introduce the Chern-Simons theory on the lattice which is expected to reproduce the results of the continuous theory exactly. The lattice model enjoys the symmetry with respect to a quantum gauge group. Using this fact we construct the algebra of observables of the Hamiltonian Chern-Simons theory equipped with a *- operation and a positive inner product.read more
Citations
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Quantization of Lie bialgebras, II
Pavel Etingof,David Kazhdan +1 more
TL;DR: In this paper, the authors give a positive answer to a number of Drinfeld's questions, using the methods and ideas of [KL], and show the existence of a quantization for Lie bialgebras.
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Non-commutative worldvolume geometries: D-branes on SU(2) and fuzzy spheres
TL;DR: In this paper, the authors explore the quantization of world-volume geometries in a curved background with non-zero Neveu-Schwarz 3-form field strength H = dB.
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Ponzano-Regge model revisited I: Gauge fixing, observables and interacting spinning particles
TL;DR: In this paper, the Ponzano-Regge model was used to properly fix all the symmetries of the 3D quantum gravity model, and the construction of the transition amplitudes in the presence of interacting quantum spinning particles was given.
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Quantization of Teichmüller spaces and the quantum dilogarithm
TL;DR: In this article, the Hamiltonian reduction of a finite-dimensional symplectic space where the mapping class group acts by symplectic rational transformations is realized as a Hamiltonian representation of the Teichmuller space of punctured surfaces.
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Three-dimensional loop quantum gravity: physical scalar product and spin-foam models
Karim Noui,Alejandro Perez +1 more
TL;DR: In this article, the dynamics in three-dimensional loop quantum gravity with zero cosmological constant were studied and a rigorous definition of Rovelli's generalized projection operator from the kinematical Hilbert space to the physical Hilbert space was provided.
References
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Book
Quantum Groups
TL;DR: In this paper, the authors introduce the theory of quantum groups with emphasis on the spectacular connections with knot theory and Drinfeld's recent fundamental contributions and present the quantum groups attached to SL2 as well as the basic concepts of the Hopf algebras.
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Quantum field theory and the Jones polynomial
TL;DR: In this paper, it was shown that 2+1 dimensional quantum Yang-Mills theory with an action consisting purely of the Chern-Simons term is exactly soluble and gave a natural framework for understanding the Jones polynomial of knot theory in three dimensional terms.
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Current Algebra and Wess-Zumino Model in Two-Dimensions
TL;DR: In this article, the anomalous dimensions of the Wess-Zumino fields are found exactly, and the multipoint correlation functions are shown to satisfy linear differential equations, in particular, Witten's non-abelean bosonisation rules are proven.
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Invariants of 3-manifolds via link polynomials and quantum groups
TL;DR: In this paper, the authors construct topological invariants of compact oriented 3-manifolds and of framed links in such manifolds, where the terms of the sequence are equale to the values of the Jones polynomial of the link in the corresponding roots of 1.
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Fusion Rules and Modular Transformations in 2D Conformal Field Theory
TL;DR: In this paper, the authors studied conformal field theories with a finite number of primary fields with respect to some chiral algebra and showed that the fusion rules are completely determined by the behavior of the characters under the modular group.