Integration over matrix spaces with unique invariant measures

Prosen, T.; Seligman, T. H.; Weidenmüller, H. A.

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Integration over matrix spaces with unique invariant measures

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Seligman, T. H.
Prof. Hans A. Weidenmüller, Emeriti, MPI for Nuclear Physics, Max Planck Society;

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Weidenmüller, H. A.
Prof. Hans A. Weidenmüller, Emeriti, MPI for Nuclear Physics, Max Planck Society;

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Prosen, T., Seligman, T. H., & Weidenmüller, H. A. (2002). Integration over matrix spaces with unique invariant measures. Journal of Mathematical Physics, 43(10), 5135-5144.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0011-84E9-3

Abstract

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, where N is the dimension of the matrix and where α is independent of the degree of the monomial. We give a lower bound on the integer and show how α 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.