Flow Equations without Mean Field Ambiguity

Abstract

We compare different methods used for non-perturbative calculations in strongly interacting fermionic systems. Mean field theory often shows a basic ambiguity related to the possibility to perform Fierz transformations. The results may then depend strongly on an unphysical parameter which reflects the choice of the mean field, thus limiting the reliability. This ambiguity is absent for Schwinger-Dyson equations or fermionic renormalization group equations. Also renormalization group equations in a partially bosonized setting can overcome the Fierz ambiguity if the truncation is chosen appropriately. This is reassuring since the partially bosonized renormalization group approach constitutes a very promising basis for the explicit treatment of condensates and spontaneous symmetry breaking even for situations where the bosonic correlation length is large.

New version to match the one published in PRD. New title (former title: Solving Mean Field Ambiguity by Flow Equations), added section IX and appendix B. More explanations in the introduction and conclusions. 16 pages, 6 figures and 3 tables uses revtex4

References in corpus (2)

• Exact evolution equation for the effective potential
• Renormalization Flow of Bound States

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