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

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 2 3 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 07 v 1 3 S ep 2 00 4 Continuity with respect to Disorder of the Integrated Density of States

We prove that the integrated density of states (IDS) associated to a random Schrödinger operator is locally uniformly Hölder continuous as a function of the disorder parameter λ. In particular, we obtain convergence of the IDS, as λ → 0, to the IDS for the unperturbed operator at all energies for which the IDS for the unperturbed operator is continuous in energy.

ar X iv : 0 80 9 . 01 74 v 1 [ m at h - ph ] 1 S ep 2 00 8 Heisenberg relations in the general case

The Heisenberg relations are derived in a quite general setting when the field transformations are induced by three representations of a given group. They are considered also in the fibre bundle approach. The results are illustrated in a case of transformations induced by the Poincaré group.

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