A conjecture on Hubbard-Stratonovich transformations for the Pruisken-Schäfer parameterisations of real hyperbolic domains

Abstract

Rigorous justification of the Hubbard-Stratonovich transformation for the Pruisken-Schäfer type of parameterisations of real hyperbolic O(m,n)-invariant domains remains a challenging problem. We show that a naive choice of the volume element invalidates the transformation, and put forward a conjecture about the correct form which ensures the desired structure. The conjecture is supported by complete analytic solution of the problem for groups O(1,1) and O(2,1), and by a method combining analytical calculations with a simple numerical evaluation of a two-dimensional integral in the case of the group O(2,2).

Published version

References in corpus (2)

• The supersymmetry method of random matrix theory
• Symmetry classes in random matrix theory