Hubbard-Stratonovich Transformation: Successes, Failure, and Cure
نویسنده
چکیده
We recall the successes of the Hubbard-Stratonovich Transformation (HST) of many-body theory, point out its failure to cope with competing channels of collective phenomena and show how to overcome this by Variational Perturbation Theory. That yields exponentially fast converging results, thanks to the help of a variety of collective classical fields, rather than a fluctuating collective quantum field as suggested by the HST. c © Electronic Journal of Theoretical Physics. All rights reserved.
منابع مشابه
A discrete Hubbard-Stratonovich decomposition for general, fermionic two-body interactions
A scheme is presented to decompose the exponential of a two-body operator in a discrete sum over exponentials of one-body operators. This discrete decomposition can be used instead of the Hubbard-Stratonovich transformation in auxiliary-field quantum Monte-Carlo methods. As an illustration, the decomposition is applied to the Hubbard model, where it is equivalent to the discrete Hubbard-Straton...
متن کاملComparison of the superbosonization formula and the generalized Hubbard–Stratonovich transformation
Recently, two different approaches were put forward to extend the supersymmetry method in random matrix theory from Gaussian ensembles to general rotation invariant ensembles. These approaches are the generalized Hubbard– Stratonovich transformation and the superbosonization formula. Here, we prove the equivalence of both approaches. To this end, we reduce integrals over functions of supersymme...
متن کاملA 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...
متن کاملar 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...
متن کاملar 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...
متن کامل