Hubbard-Stratonovich transformations

I. V. Yurkevich

O. Gunnarsson, Erik Koch

Sandro Sorella

Nguyen Van Hoa, Nguyen Tri Lan

The Hubbard - Stratonovich transformation of many - body theory is reconsidered in various versions. Learning from its failures in coping with competing channels of collective phenomena, a combined Hubbard - Stratonovich transformation is proposed to overcome these difficulties. That yields a variety of fluctuating bosonic quantum fields describing the competition of different phases in the system under consideration. As a consequence of results, the validity of the Hubbard - Stratonovich transformation and its relation to a given order parameter are discussed.

Yan V Fyodorov

We discuss and prove the validity of the Hubbard–Stratonovich (HS) identities over hyperbolic domains which are used frequently in 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 model avoiding the use of the HS transformations.