Instantons of two-dimensional fermionic effective actions by inverse scattering transformation
type: Item
instance of: scholarly article
title: Instantons of two-dimensional fermionic effective actions by inverse scattering transformation
zbMATH Open document ID: 0594.35085
DOI: 10.1007/BF01209295
published in: Communications in Mathematical Physics
publication date: 1985-01-01T00:00:00Z
review text: A method to find symmetric solutions of the nonlinear and nonlocal saddle-point equations for the effective actions, containing the logarithm of a functional Dirac determinant, which appear in 1/N expansions of fermionic theories is proposed. This method consists in using the scattering data of the rotationally symmetric Dirac equation in two dimensions with the angular momentum as a spectral parameter. The method is applied to fermionic models with quartic coupling. It is shown that the effective action that generates the 1/N expansion admits a closed form in terms of the scattering data only in the particular case of Gross-Neveu and Chiral Gross-Neveu models. No instanton solutions are present in these two models. This fact suggested that the 1/N expansion could be convergent.
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 81T08
Mathematics Subject Classification ID: 81U99
zbMATH DE Number: 3955583
zbMATH Keywords: symmetric solutions
zbMATH Keywords: saddle-point equations
zbMATH Keywords: effective actions
zbMATH Keywords: fermionic theories
zbMATH Keywords: scattering data
zbMATH Keywords: rotationally symmetric Dirac equation
zbMATH Keywords: instanton solutions
author: J. Avan
author: H. J. de Vega
reviewed by: B. Konopelchenko
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3955583