Integrals of monomials over the orthogonal group

Details Integrals of monomials over the orthogonal group Integrals of monomials over the orthogonal group

2001-12-07

arxiv.org/abs/math-ph/0112012v1

J. Math. Phys. 43, 3342-3351 (2002)

Physics

Mathematical Physics

9 pages, no figures

Scientific paper

10.1063/1.1471367

A recursion formula is derived which allows to evaluate invariant integrals over the orthogonal group O(N), where the integrand is an arbitrary finite monomial in the matrix elements of the group. The value of such an integral is expressible as a finite sum of partial fractions in $N$. The recursion formula largely extends presently available integration formulas for the orthogonal group.

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