2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/157015Rigorous 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 versionMathematical Physicstext