Hierarchies of invariant spin models

Details Hierarchies of invariant spin models Hierarchies of invariant spin models

2000-08-04

arxiv.org/abs/gr-qc/0008011v2

Nucl.Phys.B619:654-688,2001

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

42 pages, 25 figures

Scientific paper

10.1016/S0550-3213(00)00729-X

In this paper we present classes of state sum models based on the recoupling theory of angular momenta of SU(2) (and of its q-counterpart $U_q(sl(2))$, q a root of unity). Such classes are arranged in hierarchies depending on the dimension d, and include all known closed models, i.e. the Ponzano-Regge state sum and the Turaev-Viro invariant in dimension d=3, the Crane-Yetter invariant in d=4. In general, the recoupling coefficient associated with a d-simplex turns out to be a $\{3(d-2)(d+1)/2\}j$ symbol, or its q-analog. Each of the state sums can be further extended to compact triangulations $(T^d,\partial T^d)$ of a PL-pair $(M^d,\partial M^d)$, where the triangulation of the boundary manifold is not keeped fixed. In both cases we find out the algebraic identities which translate complete sets of topological moves, thus showing that all state sums are actually independent of the particular triangulation chosen. Then, owing to Pachner's theorems, it turns out that classes of PL-invariant models can be defined in any dimension d.

Affiliated with

Also associated with

No associations

Rating

Hierarchies of invariant spin models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hierarchies of invariant spin models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hierarchies of invariant spin models will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-344076