Results 21 to 30 of about 1,522 (82)

Modified Turaev-Viro invariants from quantum \(\mathfrak{sl}(2|1)\) [PDF]

Journal of Knot Theory and Its Ramifications, 2020
The main result of this paper is that the category of finite-dimensional modules over \(U_q(\mathfrak{sl}(2|1))\) can be converted, in a systematic way, into a ``relative \(G\)-spherical category'', where \(G = \mathbb{C}/\mathbb{Z}\). The usual construction of spherical fusion categories from quantum groups involves specializing \(q\) to a root of ...
Anghel, Cristina Ana-Maria, Geer, Nathan
openaire   +3 more sources

Growth of Turaev–Viro invariants and cabling [PDF]

Journal of Knot Theory and Its Ramifications, 2019
The Chen–Yang volume conjecture [Q. Chen and T. Yang, Volume conjectures for the Reshetikhin–Turaev and the Turaev–Viro invariants, preprint (2015), arXiv:1503.02547] states that the growth rate of the Turaev–Viro invariants of a compact oriented [Formula: see text]-manifold determines its simplicial volume.
openaire   +3 more sources

Quantum invariants of periodic three-manifolds [PDF]

, 1999
Let p be an odd prime and r be relatively prime to p. Let G be a finite p-group. Suppose an oriented 3-manifold M-tilde has a free G-action with orbit space M. We consider certain Witten-Reshetikhin-Turaev SU(2) invariants w_r(M).
Gilmer, Patrick M.
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3-Dimensional Gravity and the Turaev-Viro Invariant [PDF]

Progress of Theoretical Physics Supplement, 1992
We derived an asymptotic formula for q-6j symbol. This is a generalization of the former work by Ponzano and Regge. Studying the q-deformed su(2) spin network as a 3-dimensional quantum gravity model, we show that the Turaev-Viro invariant defines naturally regularized path-integral a la Ponzano-Regge in the semi-classical continuum limit.
Shun'ya Mizoguchi, Tsukasa Tada
openaire   +1 more source

Discrete Space-Time Volume for 3-Dimensional BF Theory and Quantum Gravity

, 1998
The Turaev-Viro state sum invariant is known to give the transition amplitude for the three dimensional BF theory with cosmological term, and its deformation parameter hbar is related with the cosmological constant via hbar=sqrt{Lambda}.
Ashtekar A, Ashtekar A, Baez J, Carlip S, Daughton A, Freidel L, Hawking S, Kirill Krasnov, Laurent Freidel, Ponzano G, Reshetikhin N, Rovelli C, the appendix of Freidel L, Thiemann T, Witten E   +14 more
core   +1 more source

Spin Foam Diagrammatics and Topological Invariance [PDF]

, 2001
We provide a simple proof of the topological invariance of the Turaev-Viro model (corresponding to simplicial 3d pure Euclidean gravity with cosmological constant) by means of a novel diagrammatic formulation of the state sum models for quantum BF ...
Alejandro Perez, Baez J C, Barrett J W, Florian Girelli, Freidel L, Freidel L, Markopoulou F, Massey W S, Oeckl R, Oeckl R, Pachner U, Perez A, Ponzano G, Reisenberger M, Reisenberger M, Reshetikhin N Yu, Robert Oeckl, Rourke C, Turaev V G, Zapata J A   +19 more
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2D Conformal Field Theories and Holography [PDF]

, 2002
It is known that the chiral part of any 2d conformal field theory defines a 3d topological quantum field theory: quantum states of this TQFT are the CFT conformal blocks.
Alekseev A. Yu., Alekseev A. Yu., Alekseev A. Yu., Alekseev A. Yu., Benedetti R., Boulatov D. V., Buffenoir E., Chekhov L., Felder G., Felder G., Fock V. V., Frohlich J., Fuchs J., Guadagnini E., Kashaev R. M., Kirill Krasnov, Krasnov K., Laurent Freidel, Penner R. C., Witten E.   +19 more
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Compact phase space, cosmological constant, discrete time [PDF]

, 2015
We study the quantization of geometry in the presence of a cosmological constant, using a discretiza- tion with constant-curvature simplices. Phase space turns out to be compact and the Hilbert space finite dimensional for each link.
Rovelli, Carlo, Vidotto, Francesca
core   +4 more sources

Observables in 3-dimensional quantum gravity and topological invariants

, 2004
In this paper we report some results on the expectation values of a set of observables introduced for 3-dimensional Riemannian quantum gravity with positive cosmological constant, that is, observables in the Turaev-Viro model.
Barrett J W, Barrett J W, Barrett J W García-Islas J M Martins J F, Beliakova A, Freidel L Louapre D, García-Islas J M, J Manuel García-Islas, Karowski M, Kauffman L H, Pachner U, Ponzano G   +10 more
core   +1 more source

Computations of Turaev-Viro-Ocneanu Invariants of 3-Manifolds from Subfactors [PDF]

Journal of Knot Theory and Its Ramifications, 2003
In this paper, we establish a rigorous correspondence between the two tube algebras, that one comes from the Turaev-Viro-Ocneanu TQFT introduced by Ocneanu and another comes from the sector theory introduced by Izumi, and construct a canonical isomorphism between the centers of the two tube algebras, which is a conjugate linear isomorphism preserving ...
Sato, Nobuya, Wakui, Michihisa
openaire   +3 more sources