A conjecture on Hubbard Stratonovich transformations for the Pruisken Schäfer parameterizations of real hyperbolic domains
Abstract
Rigorous justification of the Hubbard-Stratonovich transformation for the Pruisken-Schäfer type of parametrizations 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 a 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).
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- November 2007
- DOI:
- 10.1088/1751-8113/40/45/007
- arXiv:
- arXiv:math-ph/0703001
- Bibcode:
- 2007JPhA...4013587W
- Keywords:
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- Mathematical Physics
- E-Print:
- Published version