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Vassiliev Invariants for Links from Chern-Simons Perturbation Theory
The general structure of the perturbative expansion of the vacuum expectation
value of a product of Wilson-loop operators is analyzed in the context of
Chern-Simons gauge theory. Wilson loops are opened into Wilson lines in order
to unravel the algebraic structure encoded in the group factors of the
perturbative series expansion. In the process a factorization theorem is proved
for Wilson lines. Wilson lines are then closed back into Wilson loops and new
link invariants of finite type are defined. Integral expressions for these
invariants are presented for the first three primitive ones of lower degree in
the case of two-component links. In addition, explicit numerical results are
obtained for all two-component links of no more than six crossings up to degree
four.Comment: 44 pages, LaTex, epsf.sty, 15 figure