Integration over matrix spaces with unique invariant measures

Details Integration over matrix spaces with unique invariant measures Integration over matrix spaces with unique invariant measures

2002-03-21

arxiv.org/abs/math-ph/0203042v1

Physics

Mathematical Physics

12 pages in revtex, no figures

Scientific paper

We present a method to calculate integrals over monomials of matrix elements with invariant measures in terms of Wick contractions. The method gives exact results for monomials of low order. For higher--order monomials, it leads to an error of order 1/N^alpha where N is the dimension of the matrix and where alpha is independent of the degree of the monomial. We give a lower bound on the integer alpha and show how alpha can be increased systematically. The method is particularly suited for symbolic computer calculation. Explicit results are given for O(N), U(N) and for the circular orthogonal ensemble.

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