On Hubbard-Stratonovich Transformations over Hyperbolic Domains
classification
🧮 math-ph
cond-mat.mes-hallhep-thmath.MP
keywords
disordereddomainshubbard-stratonovichhyperbolicmodelsystemstransformationsapart
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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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