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

Brown, Michael, and Whittingham, Ian (2015) Two-particle irreducible effective actions versus resummation: analytic properties and self-consistency. Nuclear Physics B, 900. pp. 477-500.

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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.

Item ID: 41040
Item Type: Article (Research - C1)
ISSN: 1873-1562
Keywords: quantum field theory; effective action; two-particle irreducible; resummation; asymptotic series; perturbation theory; Feynman diagram
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© 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license(http://creativecommons.org/licenses/by/4.0/). Funded by the Sponsoring Consortium for Open Access Publishing in Particle Physics (SCOAP).

A version of this publication was included in the following PhD thesis: Brown, Michael Jonathan (2017) Symmetry improvement techniques for non-perturbative quantum field theory. PhD thesis, James Cook University, which is available Open Access in ResearchOnline@JCU. Please see the Related URLs for access.

Date Deposited: 26 Oct 2015 02:08
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