Massive poles in Lee-Wick quantum field theory

Most discussions of propagators in Lee-Wick theories focus on the presence of two massive complex conjugate poles in the propagator. We show that there is, in fact, only one pole near the physical region or, in another representation, three polelike structures with compensating extra poles. The latter modified Lehmann representation is useful caculationally and conceptually only if one includes the resonance structure in the spectral integral. We treat both the photon propagator in Lee-Wick electrodynamics and the spin-two propagator in quadratic gravity.