  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.
