Linear response theory for symmetry improved two particle irreducible effective actions

Brown, Michael;Whittingham, Ian B.;Kosov, Daniel S.

Abstract

We investigate the linear response of an O(N) scalar quantum field theory subject to external perturbations using the symmetry-improved two-particle irreducible effective action (SI-2PIEA) formalism [A. Pilaftsis and D. Teresi, Nucl. Phys. B874, 594 (2013)]. Despite satisfactory equilibrium behavior, we find a number of unphysical effects at the linear response level. Goldstone boson field fluctuations are overdetermined, with the only consistent solution being to set the fluctuations and their driving sources to zero, except for momentum modes where the Higgs and Goldstone self-energies obey a particular relationship. Also Higgs field fluctuations propagate masslessly, despite the Higgs propagator having the correct mass. These pathologies are independent of any truncation of the effective action and still exist even if we relax the overdetermining Ward identities, so long as the constraint is formulated O(N) covariantly. We discuss possible reasons for the apparent incompatibility of the constraints and linear response approximation and possible ways forward.

Journal

Physical Review D

Publication Name

N/A

Volume

ISBN/ISSN

1089-4918

Edition

N/A

Issue

Pages Count

Location

N/A

Publisher

American Physical Society

Publisher Url

N/A

Publisher Location

N/A

Publish Date

N/A

Url

N/A

Date

N/A

EISSN

N/A

DOI

10.1103/PhysRevD.93.105018