1,955 research outputs found
Characterizing partition functions of the edge-coloring model by rank growth
We characterize which graph invariants are partition functions of an
edge-coloring model over the complex numbers, in terms of the rank growth of
associated `connection matrices'
Graph Invariants of Vassiliev Type and Application to 4D Quantum Gravity
We consider a special class of Kauffman's graph invariants of rigid vertex
isotopy (graph invariants of Vassiliev type). They are given by a functor from
a category of colored and oriented graphs embedded into a 3-space to a category
of representations of the quasi-triangular ribbon Hopf algebra . Coefficients in expansions of them with respect to () are
known as the Vassiliev invariants of finite type. In the present paper, we
construct two types of tangle operators of vertices. One of them corresponds to
a Casimir operator insertion at a transverse double point of Wilson loops. This
paper proposes a non-perturbative generalization of Kauffman's recent result
based on a perturbative analysis of the Chern-Simons quantum field theory. As a
result, a quantum group analog of Penrose's spin network is established taking
into account of the orientation. We also deal with the 4-dimensional canonical
quantum gravity of Ashtekar. It is verified that the graph invariants of
Vassiliev type are compatible with constraints of the quantum gravity in the
loop space representation of Rovelli and Smolin.Comment: 34 pages, AMS-LaTeX, no figures,The proof of thm.5.1 has been
improve
- …