VASSILIEV INVARIANTS FOR LINKS FROM CHERN-SIMONS PERTURBATION-THEORY

The general structure of the perturbative expansion of the vacuum expe ctation value of a product of Wilson-loop operators is analyzed in the context of Chem-Simons gauge theory, Wilson loops are opened into Wil son lines in order to unravel the algebraic structure encoded in the g roup factors of the perturbative series expansion. In the process a fa ctorization theorem is proved for Wilson lines. Wilson lines are then closed back into Wilson loops and new link invariants of finite type a re defined. Integral expressions for these invariants are presented fo r the first three primitive ones of lower degree in the case of two-co mponent links. In addition, explicit numerical results are obtained fo r all two-component links of no more than six crossings up to degree f our. (C) 1997 Elsevier Science B.V.