A conjecture on Hubbard-Stratonovich transformations for the Pruisken-Schäfer parameterisations of real hyperbolic domains
arXiv:math-ph/0703001 · doi:10.1088/1751-8113/40/45/007
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).
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References in corpus (10)
- Statistics of energy levels and eigenfunctions in disordered systems
- Riemannian symmetric superspaces and their origin in random matrix theory
- Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering for systems with broken time reversal invariance
- Random Matrix Theory and Chiral Symmetry in QCD
- Negative moments of characteristic polynomials of random matrices: Ingham-Siegel integral as an alternative to Hubbard-Stratonovich transformation
- Characteristic polynomials of random Hermitian matrices and Duistermaat-Heckman localisation on non-compact Kaehler manifolds
- The supersymmetry method of random matrix theory
- WKB-expansion of the HarishChandra-Itzykson-Zuber integral for arbitrary beta
- On Hubbard-Stratonovich Transformations over Hyperbolic Domains
- Symmetry classes in random matrix theory