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

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

2010-09-06

arxiv.org/abs/1009.1094v2

Phys.Rev.D82:094023,2010

Physics

High Energy Physics

High Energy Physics - Phenomenology

9 pages, to appear on Phys. Rev. D

Scientific paper

10.1103/PhysRevD.82.094023

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.

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