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A conjecture on Hubbard–Stratonovich transformations for the Pruisken–Schäfer parameterizations of real hyperbolic domains

2007/03/31 by Y. Wei, Yi Wei, Yan V. Fyodorov +1 · 1 citation
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Mathematics and Applications #Quantum chaos and dynamical systems #math-ph #math.MP

paper · pdf · doi:10.1088/1751-8113/40/45/007

published as J. Phys. A, Vol 40 (2007) 13587-13605 · Published version

openalex publication_date 2007/10/23 · arxiv created 2008/03/18 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

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).

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