Some comments on ghosts and unitarity: The Pais-Uhlenbeck oscillator revisited

Abstract

We give a simple discussion of ghosts, unitarity violation, negative norm states, and quantum vs classical behavior in the simplest model with a four-derivative action---the Pais-Uhlenbeck oscillator. We also point out that the normalizable ``vacuum state'' (in the sense defined below) of this model can be understood as a spontaneous breaking of the emergent conformal symmetry. We provide an example of an interacting system that couples the ``particle'' and ``ghost'' degrees of freedom and nevertheless remains unitary on both the classical and quantum levels.