Integration over angular variables for two coupled matrices

G. Mahoux (1) , M.L. Mehta (1) , J.-M. Normand (1)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681

An integral over the angular variables for two coupled $n$ x $n$ real symmetric, complex hermitian or quaternion self-dual matrices is expressed in term of the eigenvalues and eigenfunctions of a hamiltonian closely related to the Calogero hamiltinian. This generalizes the known result for the complex hermitian matrices. The integral can thus be evaluated for $n = 2$ and reduced to a single sum for $n = 3$

Domaines: Physique mathématique [math-ph]

G. Mahoux, M.L. Mehta, J.-M. Normand. Integration over angular variables for two coupled matrices. Pavel Bleher; Alexander Its. Random Matrix Models and Their Applications, 40, Cambridge UP, pp.301-320, 2001, MSRI Publications, 0-521-80209-1. ⟨cea-02905122⟩