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

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.

REVTEX, 7 figures (available upon request), IFT-P.037/93, DOE/ER/40427-12-N93

References in corpus (2)

• Gauge covariance and the fermion-photon vertex in three- and four- dimensional, massless quantum electrodynamics
• Ghost Poles in the Nucleon Propagator: Vertex Corrections and Form Factors

Cited by in corpus (9)

• The pion: an enigma within the Standard Model
• Perspective on the origin of hadron masses
• Empirical Consequences of Emergent Mass
• Quark propagator in Minkowski space
• Baryons and the Borromeo
• Consistent off-shell $\pi NN$ vertex and nucleon self-energy
• Ghost poles in the nucleon propagator in the linear-sigma model approach and its role in pion-nucleon low-energy theorems
• Coupled Dyson-Schwinger Equations and Effects of Self-Consistency
• Vector Meson Propagator and Baryon Current Conservation