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Self-consistent solution of the Schwinger-Dyson equations for the nucleon and meson propagators

M. E. Bracco·A. Eiras·G. Krein·L. Wilets
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Abstract

The Schwinger-Dyson equations for the nucleon and meson propagators are solved self-consistently in an approximation that goes beyond the Hartree-Fock approximation. The traditional approach consists in solving the nucleon Schwinger-Dyson equation with bare meson propagators and bare meson-nucleon vertices; the corrections to the meson propagators are calculated using the bare nucleon propagator and bare nucleon-meson vertices. It is known that such an approximation scheme produces the appearance of ghost poles in the propagators. In this paper the coupled system of Schwinger-Dyson equations for the nucleon and the meson propagators are solved self-consistently including vertex corrections. The interplay of self-consistency and vertex corrections on the ghosts problem is investigated. It is found that the self-consistency does not affect significantly the spectral properties of the propagators. In particular, it does not affect the appearance of the ghost poles in the propagators.

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M. E. Bracco, A. Eiras, G. Krein, L. Wilets. 1993-07-07. Self-consistent solution of the Schwinger-Dyson equations for the nucleon and meson propagators. https://doi.org/10.1103/physrevc.49.1299

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