Constraining the effective action by a method of external sources

Abstract: 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.