On aspects of self-consistency in the Dyson-Schwinger approach to QED and λ(ϕ^\star ϕ)^2 theories

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 non-perturbative solution of the gap equation for the self-interacting scalar field theory.

arXiv comment9 pages, to appear on Phys. Rev. D

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Cited by in corpus (3)

• Techniques for n-Particle Irreducible Effective Theories
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• Hedin equations in resonant micro-cavities