Some Comments on Ghosts and Unitarity: The Pais-Uhlenbeck Oscillator Revisited

Understand

We give a simple discussion of ghosts, unitarity violation, negative norm states and quantum vs classical behavior in the simplest model with 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 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 classical and quantum level.