Abstract
We investigate some aspects of the self-consistency in the Dyson-Schwinger approach to both the QED and the self-interacting scalar field theories. We prove that the set of the Dyson-Schwinger equations, together with the Green-Ward-Takahashi identity, is equivalent to the analogous set of integral equations studied in condensed matter, namely, many-body perturbation theory, where it is solved self-consistently and iteratively. In this framework, we compute the nonperturbative solution of the gap equation for the self-interacting scalar field theory.
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