Knots, Feynman Diagrams and Matrix Models

Abstract

An U(N)-invariant matrix model with d matrix variables is studied. It was shown that in the limit $N\to \infty$ and $d\to 0$ the model describes the knot diagrams. We realize the free partition function of the matrix model as the generalized expectation of a Hida distribution ${\Phi }_{N,d}$. This enables us to give a mathematically rigorous meaning to the partition function with interaction. For the generalized function ${\Phi }_{N,d}$ we prove a Wick theorem and we derive explicit formulas for the propagators.

31 pages, 6 Postscript figures