Results 31 to 40 of about 1,460 (82)

(3+1)-dimensional topological phases and self-dual quantum geometries encoded on Heegard surfaces

, 2017
We apply the recently suggested strategy to lift state spaces and operators for (2+1)-dimensional topological quantum field theories to state spaces and operators for a (3+1)-dimensional TQFT with defects.
Dittrich, Bianca
core   +1 more source

Discrete structures in gravity [PDF]

, 2000
Discrete approaches to gravity, both classical and quantum, are reviewed briefly, with emphasis on the method using piecewise-linear spaces. Models of 3-dimensional quantum gravity involving 6j-symbols are then described, and progress in generalising ...
Ambjørn J., Archer F. J., Baez J., Baez J., Barrett J. W., Barrett J. W., Barrett J. W., Barrett J. W., Barrett J. W., Barrett J. W., Barrett J. W., Birmingham D., Birmingham D., Brewin L., Brewin L., Carfora M., Caselle M., Correia da Silva C. L. B., Correia da Silva C. L. B., Franzosi R., Franzosi R., Freidel L., Freidel L., Gott J. R., Hamber H. W., Hamber H. W., Hartle J. B., Hasslacher B., Hollmann H. R., Immirzi G., Ionicioiu R., Ionicioiu R., Iwasaki J., Kauffman L. H., Mannion C. L., Markopoulou F., Markopoulou F., Menotti P., Ooguri H., Reisenberger M., Reisenberger M., Reisenberger M., Riedler J., Roberts J. D., Roček M., Ruth M. Williams, Schleich K., Schleich K., Tullio Regge, Turaev V. G., Waelbroeck H., Welling M., Williams R. M., ’t Hooft G., ’t Hooft G.   +54 more
core   +2 more sources

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

Asymptotics of quantum 6j$6j$‐symbols and generalized hyperbolic tetrahedra

Journal of Topology, Volume 18, Issue 3, September 2025.
Abstract We establish the geometry behind the quantum 6j$6j$‐symbols under only the admissibility conditions as in the definition of the Turaev–Viro invariants of 3‐manifolds. As a classification, we show that the 6‐tuples in the quantum 6j$6j$‐symbols give in a precise way to the dihedral angles of (1) a spherical tetrahedron, (2) a generalized ...
Giulio Belletti, Tian Yang
wiley   +1 more source

Braiding and entanglement in spin networks: a combinatorial approach to topological phases

, 2008
The spin network quantum simulator relies on the su(2) representation ring (or its q-deformed counterpart at q= root of unity) and its basic features naturally include (multipartite) entanglement and braiding.
Kadar, Zoltan, Marzuoli, Annalisa, Rasetti, Mario   +2 more
core   +1 more source

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

Asymptotic Behavior of Colored Jones polynomial and Turaev-Viro Invariant of figure eight knot

, 2020
In this paper we investigate the asymptotic behavior of the colored Jones polynomials and the Turaev-Viro invariants for the figure eight knot. More precisely, we consider the $M$-th colored Jones polynomials evaluated at $(N+1/2)$-th root of unity with ...
Au, Thomas Kwok-Keung, Wong, Ka Ho
core  

Topological invariants from non-restricted quantum groups

, 2013
We introduce the notion of a relative spherical category. We prove that such a category gives rise to the generalized Kashaev and Turaev-Viro-type 3-manifold invariants defined in arXiv:1008.3103 and arXiv:0910.1624, respectively.
Bertrand Patureau-Mirand, De Concini, De Concini, Geer, Nathan Geer, Neumann, Turaev   +6 more
core   +3 more sources

A manifestly Morita-invariant construction of Turaev–Viro invariants

Quantum Topology
We present a state sum construction that assigns a scalar to a skeleton in a closed oriented three-dimensional manifold. The input datum is the pivotal bicategory \mathbf{Mod}^{\mathrm{sph}}(\mathcal{A}) of spherical module categories over a ...
Jürgen Fuchs, César Galindo, David Jaklitsch, Christoph Schweigert   +3 more
openaire   +2 more sources

Turaev-Viro invariants as an extended TQFT

, 2010
38 pages, many figures. New in v.3: significantly rewritten exposition, providing details of some proofs which were only outlined in the previous ...
Kirillov Jr., Alexander, Balsam, Benjamin   +1 more
openaire   +2 more sources