A conjecture on Hubbard–Stratonovich transformations for the Pruisken–Schäfer parameterizations of real hyperbolic domains
Yi Wei, Yan V Fyodorov
2007
Journal of Physics A: Mathematical and Theoretical
Rigorous justification of the Hubbard-Stratonovich transformation for the Pruisken-Sch\"afer 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
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... ical calculations with a simple numerical evaluation of a two-dimensional integral in the case of the group O(2,2).
doi:10.1088/1751-8113/40/45/007
fatcat:6somnzrlrbg6jgx7yjtokpezcm