Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-02-28
Commun.Math.Phys. 185 (1997) 621-640
Physics
High Energy Physics
High Energy Physics - Theory
16 pages, RevTeX, 15 figures included
Scientific paper
10.1007/s002200050103
The expectation value of a Wilson loop in a Chern--Simons theory is a knot invariant. Its skein relations have been derived in a variety of ways, including variational methods in which small deformations of the loop are made and the changes evaluated. The latter method only allowed to obtain approximate expressions for the skein relations. We present a generalization of this idea that allows to compute the exact form of the skein relations. Moreover, it requires to generalize the resulting knot invariants to intersecting knots and links in a manner consistent with the Mandelstam identities satisfied by the Wilson loops. This allows for the first time to derive the full expression for knot invariants that are suitable candidates for quantum states of gravity (and supergravity) in the loop representation. The new approach leads to several new insights in intersecting knot theory, in particular the role of non-planar intersections and intersections with kinks.
Gambini Rodolfo
Pullin Jorge
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