ar X iv : m at h - ph / 0 40 90 14 v 2 3 O ct 2 00 4 On Hubbard - Stratonovich Transformations over Hyperbolic Domains

ar X iv : m at h - ph / 0 40 90 14 v 3 1 1 O ct 2 00 4 On Hubbard - Stratonovich Transformations over Hyperbolic Domains

We discuss and prove validity of the Hubbard-Stratonovich (HS) identities over hyperbolic domains which are used frequently in the studies on disordered systems and random matrices. We also introduce a counterpart of the HS identity arising in disordered systems with ”chiral” symmetry. Apart from this we outline a way of deriving the nonlinear σ-model from the gauge-invariant Wegner k−orbital m...

ar X iv : m at h - ph / 0 40 90 14 v 1 5 S ep 2 00 4 On Hubbard - Stratonovich Transformations over Hyperbolic Domains

We discuss and prove validity of the Hubbard-Stratonovich (HS) identities over hyperbolic domains which are used frequently in the studies on disordered systems and random matrices. We also introduce a counterpart of the HS identity arising in disordered systems with ”chiral” symmetry. Apart from this we outline a way of deriving the nonlinear σ-model from the gauge-invariant Wegner k−orbital m...

ar X iv : m at h - ph / 0 40 90 62 v 2 1 3 O ct 2 00 4 A remark on rational isochronous potentials

We consider the rational potentials of the one-dimensional mechanical systems, which have a family of periodic solutions with the same period (isochronous potentials). We prove that up to a shift and adding a constant all such potentials have the form U (x) = 1 2 ω 2 x 2 or U (x) = 1 8 ω 2 x 2 + c 2 x −2 .

ar X iv : h ep - l at / 0 11 00 06 v 2 3 O ct 2 00 1 1 Matrix elements of ∆ S = 2 operators with Wilson fermions

A conjecture on Hubbard-Stratonovich transformations for the Pruisken-Schäfer parameterisations of real hyperbolic domains

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 com...