On Hubbard-Stratonovich Transformations over Hyperbolic Domains

Details On Hubbard-Stratonovich Transformations over Hyperbolic Domains On Hubbard-Stratonovich Transformations over Hyperbolic Domains

2004-09-05

arxiv.org/abs/math-ph/0409014v3

Journal of Physics:Condensed Matter v.17 (2005), S1915-S1928

Physics

Mathematical Physics

More accurate proofs are given; a few misprints are corrected; a misleading reference and a footnote in the end of section 2.2

Scientific paper

10.1088/0953-8984/17/20/018

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 $\sigma$-model from the gauge-invariant Wegner $k-$orbital model avoiding the use of the HS transformations.

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