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We investigate the linear response of an O(N) scalar quantum field theorysubject to external perturbations using the symmetry improved two particleirreducible effective action formalism [A. Pilaftsis and D. Teresi, Nucl. Phys.B874, 594 (2013)]. Despite satisfactory equilibrium behavior, we find a numberof unphysical effects at the linear response level. Goldstone boson fieldfluctuations are over-determined, with the only consistent solution being toset the fluctuations and their driving sources to zero, except for momentummodes where the Higgs and Goldstone self-energies obey a particularrelationship. Also Higgs field fluctuations propagate masslessly, despite theHiggs propagator having the correct mass. These pathologies are independent ofany truncation of the effective action and still exist even if we relax theover-determining Ward identities, so long as the constraint is formulatedO(N)-covariantly. We discuss possible reasons for the apparent incompatibilityof the constraints and linear response approximation and possible ways forward.

Linear Response Theory for Symmetry Improved Two Particle Irreducible Effective Actions