Two-particle irreducible effective actions versus resummation: analytic properties and self-consistency

Abstract

Approximations based on two-particle irreducible (2PI) effective actions (also known as $\Phi$-derivable, Cornwall-Jackiw-Tomboulis or Luttinger-Ward functionals depending on context) have been widely used in condensed matter and non-equilibrium quantum/statistical field theory because this formalism gives a robust, self-consistent, non-perturbative and systematically improvable approach which avoids problems with secular time evolution. The strengths of 2PI approximations are often described in terms of a selective resummation of Feynman diagrams to infinite order. However, the Feynman diagram series is asymptotic and summation is at best a dangerous procedure. Here we show that, at least in the context of a toy model where exact results are available, the true strength of 2PI approximations derives from their self-consistency rather than any resummation. This self-consistency allows truncated 2PI approximations to capture the branch points of physical amplitudes where adjustments of coupling constants can trigger an instability of the vacuum. This, in effect, turns Dyson's argument for the failure of perturbation theory on its head. As a result we find that 2PI approximations perform better than Padé approximation and are competitive with Borel-Padé resummation. Finally, we introduce a hybrid 2PI-Padé method.

Version accepted for publication in Nuclear Physics B. 31 pages, 16 figures. Uses feynmf

References in corpus (2)

• Nonequilibrium Quantum Fields: From Cold Atoms to Cosmology
• Symmetry Improved 2PI Effective Action and the Infrared Divergences of the Standard Model

Cited by in corpus (5)

• Addressing energy density functionals in the language of path-integrals I: Comparative study of diagrammatic techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• Soft symmetry improvement of two particle irreducible effective actions
• Linear Response Theory for Symmetry Improved Two Particle Irreducible Effective Actions
• Schwinger-Keldysh non-perturbative field theory of open quantum systems beyond the Markovian regime: Application to spin-boson and spin-chain-boson models
• Addressing energy density functionals in the language of path-integrals II: Comparative study of functional renormalization group techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory