Knots, Feynman Diagrams and Matrix Models

Details Knots, Feynman Diagrams and Matrix Models Knots, Feynman Diagrams and Matrix Models

1999-08-03

arxiv.org/abs/math/9908013v1

Mathematics

Quantum Algebra

31 pages, 6 Postscript figures

Scientific paper

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.

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