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Primitive Vassiliev Invariants and Factorization in Chern-Simons Perturbation Theory
The general structure of the perturbative expansion of the vacuum expectation
value of a Wilson line operator in Chern-Simons gauge field theory is analyzed.
The expansion is organized according to the independent group structures that
appear at each order. It is shown that the analysis is greatly simplified if
the group factors are chosen in a certain way that we call canonical. This
enables us to show that the logarithm of a polinomial knot invariant can be
written in terms of primitive Vassiliev invariants only.Comment: 15 pages, latex, 2 figure
A path integral derivation of -genus
The formula for the Hirzebruch -genus of complex manifolds is a
consequence of the Hirzebruch-Riemann-Roch formula. The classical index
formulae for Todd genus, Euler number, and Signature correspond to the case
when the complex variable 0, -1, and 1 respectively. Here we give a {\it
direct} derivation of this nice formula based on supersymmetric quantum
mechanics.Comment: 5 page
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