Constraining the effective action by a method of external sources

We propose a novel method of evaluating the effective action, wherein the physical one- and two-point functions are obtained in the limit of non-vanishing external sources. We illustrate the self-consistency of this method by recovering the usual 2PI effective action due to Cornwall, Jackiw and Tomb...

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Main Authors: Garbrecht, Björn, Millington, Peter
Format: Article
Published: Elsevier 2016
Online Access:https://eprints.nottingham.ac.uk/47782/
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author Garbrecht, Björn
Millington, Peter
author_facet Garbrecht, Björn
Millington, Peter
author_sort Garbrecht, Björn
building Nottingham Research Data Repository
collection Online Access
description We propose a novel method of evaluating the effective action, wherein the physical one- and two-point functions are obtained in the limit of non-vanishing external sources. We illustrate the self-consistency of this method by recovering the usual 2PI effective action due to Cornwall, Jackiw and Tomboulis, differing only by the fact that the saddle-point 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 non-perturbatively far away from one-another. A pertinent example is the decay of false vacua in radiatively-generated 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 two-particle-point-irreducible (2PPI) effective action of Coppens and Verschelde. Finally, in the spirit of the symmetry-improved 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 re-organized, such that the Goldstone boson remains massless algebraically in the symmetry-broken phase and we obtain the correct second-order thermal phase transition.
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spelling nottingham-477822020-05-04T17:49:13Z https://eprints.nottingham.ac.uk/47782/ Constraining the effective action by a method of external sources Garbrecht, Björn Millington, Peter We propose a novel method of evaluating the effective action, wherein the physical one- and two-point functions are obtained in the limit of non-vanishing external sources. We illustrate the self-consistency of this method by recovering the usual 2PI effective action due to Cornwall, Jackiw and Tomboulis, differing only by the fact that the saddle-point 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 non-perturbatively far away from one-another. A pertinent example is the decay of false vacua in radiatively-generated 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 two-particle-point-irreducible (2PPI) effective action of Coppens and Verschelde. Finally, in the spirit of the symmetry-improved 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 re-organized, such that the Goldstone boson remains massless algebraically in the symmetry-broken phase and we obtain the correct second-order thermal phase transition. Elsevier 2016-05-31 Article PeerReviewed Garbrecht, Björn and Millington, Peter (2016) Constraining the effective action by a method of external sources. Nuclear Physics B, 906 . pp. 105-132. ISSN 1873-1562 http://www.sciencedirect.com/science/article/pii/S0550321316000663?via%3Dihub doi:10.1016/j.nuclphysb.2016.02.022 doi:10.1016/j.nuclphysb.2016.02.022
spellingShingle Garbrecht, Björn
Millington, Peter
Constraining the effective action by a method of external sources
title Constraining the effective action by a method of external sources
title_full Constraining the effective action by a method of external sources
title_fullStr Constraining the effective action by a method of external sources
title_full_unstemmed Constraining the effective action by a method of external sources
title_short Constraining the effective action by a method of external sources
title_sort constraining the effective action by a method of external sources
url https://eprints.nottingham.ac.uk/47782/
https://eprints.nottingham.ac.uk/47782/
https://eprints.nottingham.ac.uk/47782/