A new method to calculate the n-Particle Irreducible Effective Action

Abstract

In this paper, we present a new method to calculate the n-Loop n-particle irreducible effective action. The key is an organizational trick that involves the introduction of a set of fictitious bare vertices that are set to zero at the end of the calculation. Using these fictitious vertices, we prove that the Schwinger-Dyson equations are the same as the equations of motion obtained from the n-particle irreducible effective action, up to the level at which they respect the symmetries of the original theory. This result allows us to obtain the effective action directly from the Schwinger-Dyson equations, which are comparatively easy to calculate. As a check of our method, we reproduce the known results for the n-Loop n-particle irreducible effective action with n = 4 and n = 5. We also use the technique to calculate the 6-Loop 6-particle irreducible effective action.

31 pages and 30 figures. Some sections are reorganized and typos are corrected. Final version to appear in PRD

References in corpus (6)

• Techniques for n-Particle Irreducible Effective Theories
• Nonequilibrium dynamics in the O(N) model to next-to-next-to-leading order in the 1/N expansion
• Leading Order QED Electrical Conductivity from the 3PI Effective Action
• QED Electrical Conductivity using the 2PI Effective Action
• Ward Identities for the 2PI effective action in QED
• Effective convergence of the 2PI-1/N expansion for nonequilibrium quantum fields

Cited by in corpus (8)

• Renormalization group methods and the 2PI effective action
• The 2PI effective theory at next-to-leading order using the functional renormalization group
• The 2PI effective action at four loop order in ${\phi }^4$ theory
• Bethe-Salpeter Equations from the 4PI effective action
• 4-point vertices from the 2PI and 4PI Effective Actions
• Renormalization of the 4PI effective action using the functional renormalization group
• Symmetry improvement of 3PI effective actions for O(N) scalar field theory
• Results from the 4PI Effective Action in 2- and 3-dimensions