Link Invariants of Finite Type and Perturbation Theory

Details Link Invariants of Finite Type and Perturbation Theory Link Invariants of Finite Type and Perturbation Theory

1992-07-13

arxiv.org/abs/hep-th/9207041v1

Lett.Math.Phys. 26 (1992) 43-52

Physics

High Energy Physics

High Energy Physics - Theory

11 pages

Scientific paper

10.1007/BF00420517

The Vassiliev-Gusarov link invariants of finite type are known to be closely related to perturbation theory for Chern-Simons theory. In order to clarify the perturbative nature of such link invariants, we introduce an algebra V_infinity containing elements g_i satisfying the usual braid group relations and elements a_i satisfying g_i - g_i^{-1} = epsilon a_i, where epsilon is a formal variable that may be regarded as measuring the failure of g_i^2 to equal 1. Topologically, the elements a_i signify crossings. We show that a large class of link invariants of finite type are in one-to-one correspondence with homogeneous Markov traces on V_infinity. We sketch a possible application of link invariants of finite type to a manifestly diffeomorphism-invariant perturbation theory for quantum gravity in the loop representation.

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