Numerical knot invariants of finite type from ChernSimons perturbation theory
Abstract
ChernSimons gauge theory for compact semisimple groups is analyzed from a perturbation theory point of view. The general form of the perturbative series expansion of a Wilson line is presented in terms of the Casimir operators of the gauge group. From this expansion new numerical knot invariants are obtained. These knot invariants turn out to be of finite type (Vassiliev invariants) and to possess an integral representation. Using known results about Jones, HOMFLY, Kauffman and AkutsuWadati polynomial invariants these new knot invariants are computed up to type six for all prime knots up to six crossings. Our results suggest that these knot invariants can be normalized in such a way that they are integervalued.
 Publication:

Nuclear Physics B
 Pub Date:
 February 1995
 DOI:
 10.1016/05503213(94)00430M
 arXiv:
 arXiv:hepth/9407076
 Bibcode:
 1995NuPhB.433..555A
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Quantum Algebra
 EPrint:
 58 pages