Constraining the effective action by a method of external sourcesTools Garbrecht, Björn and Millington, Peter (2016) Constraining the effective action by a method of external sources. Nuclear Physics B, 906 . pp. 105132. ISSN 18731562
AbstractWe propose a novel method of evaluating the effective action, wherein the physical one and twopoint functions are obtained in the limit of nonvanishing external sources. We illustrate the selfconsistency of this method by recovering the usual 2PI effective action due to Cornwall, Jackiw and Tomboulis, differing only by the fact that the saddlepoint evaluation of the path integral is performed along the extremal quantum, rather than classical, path. As such, this approach is of particular relevance to situations where the dominant quantum and classical paths are nonperturbatively far away from oneanother. A pertinent example is the decay of false vacua in radiativelygenerated potentials, as may occur for the electroweak vacuum of the Standard Model. In addition, we describe how the external sources may instead be chosen so as to yield the twoparticlepointirreducible (2PPI) effective action of Coppens and Verschelde. Finally, in the spirit of the symmetryimproved effective action of Pilaftsis and Teresi, we give an example of how the external sources can be used to preserve global symmetries in truncations of the 2PI effective action. Specifically, in the context of an O(2) model with spontaneous symmetry breaking, we show that this approach allows the Hartree–Fock approximation to be reorganized, such that the Goldstone boson remains massless algebraically in the symmetrybroken phase and we obtain the correct secondorder thermal phase transition.
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