Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spin Networks, Turaev-Viro Theory and the Loop Representation   We investigate the Ponzano-Regge and Turaev-Viro topological field theories
using spin networks and their $q$-deformed analogues. I propose a new
description of the state space for the Turaev-Viro theory in terms of skein
space, to which $q$-spin networks belong, and give a similar description of the
Ponzano-Regge state space using spin networks.
  I give a definition of the inner product on the skein space and show that
this corresponds to the topological inner product, defined as the manifold
invariant for the union of two 3-manifolds.
  Finally, we look at the relation with the loop representation of quantum
general relativity, due to Rovelli and Smolin, and suggest that the above inner
product may define an inner product on the loop state space.

2
The categories of this paper are: math
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph