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Instantons of two-dimensional fermionic effective actions by inverse scattering transformation. (English) Zbl 0594.35085

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.
Reviewer: B.Konopelchenko

MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
81T08 Constructive quantum field theory
81U99 Quantum scattering theory
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