Techniques for n-Particle Irreducible Effective Theories

Abstract

In this paper we show that the skeleton diagrams in the m-Loop nPI effective action correspond to an infinite resummation of perturbative diagrams which is void of double counting at the m-Loop level. We also show that the variational equations of motion produced by the n-Loop nPI effective theory are equivalent to the Schwinger-Dyson equations, up to the order at which they are consistent with the underlying symmetries of the original theory. We use a diagrammatic technique to obtain the 5-Loop 5PI effective action for a scalar theory with cubic and quartic interactions, and verify that the result satisfies these two statements.

43 pages, 48 figures, add a paragraph in conclusions, Figs. 25,45,46 changed, typos corrected, final version to appear in PRD

References in corpus (3)

• Pinch Technique: Theory and Applications
• Ward Identities for the 2PI effective action in QED
• On aspects of self-consistency in the Dyson-Schwinger approach to QED and λ(ϕ^\star ϕ)^2 theories

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