Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-07-20
J.Math.Phys. 41 (2000) 2658-2699
Physics
High Energy Physics
High Energy Physics - Theory
73 pages, latex, epsf, 18 figures, 2 tables
Scientific paper
10.1063/1.533311
We analyse the perturbative series expansion of the vacuum expectation value of a Wilson loop in Chern-Simons gauge theory in the temporal gauge. From the analysis emerges the notion of the kernel of a Vassiliev invariant. The kernel of a Vassiliev invariant of order n is not a knot invariant, since it depends on the regular knot projection chosen, but it differs from a Vassiliev invariant by terms that vanish on knots with n singular crossings. We conjecture that Vassiliev invariants can be reconstructed from their kernels. We present the general form of the kernel of a Vassiliev invariant and we describe the reconstruction of the full primitive Vassiliev invariants at orders two, three and four. At orders two and three we recover known combinatorial expressions for these invariants. At order four we present new combinatorial expressions for the two primitive Vassiliev invariants present at this order.
Labastida Jose M. F.
Perez Esther
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