Twoparticle irreducible effective actions versus resummation: analytic properties and selfconsistency
Brown, Michael, and Whittingham, Ian (2015) Twoparticle irreducible effective actions versus resummation: analytic properties and selfconsistency. Nuclear Physics B, 900. pp. 477500.

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Abstract
Approximations based on twoparticle irreducible (2PI) effective actions (also known as \Phiderivable, Cornwall–Jackiw–Tomboulis or Luttinger–Ward functionals depending on context) have been widely used in condensed matter and nonequilibrium quantum/statistical field theory because this formalism gives a robust, selfconsistent, nonperturbative 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 selfconsistency rather than any resummation. This selfconsistency 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:  18731562 
Keywords:  quantum field theory; effective action; twoparticle irreducible; resummation; asymptotic series; perturbation theory; Feynman diagram 
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Additional Information:  © 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 nonperturbative 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 
FoR Codes:  01 MATHEMATICAL SCIENCES > 0105 Mathematical Physics > 010505 Mathematical Aspects of Quantum and Conformal Field Theory, Quantum Gravity and String Theory @ 33% 02 PHYSICAL SCIENCES > 0206 Quantum Physics > 020602 Field Theory and String Theory @ 34% 01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics > 010201 Approximation Theory and Asymptotic Methods @ 33% 
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