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

TL;DR

This paper revisits the Pais-Uhlenbeck oscillator to analyze ghosts, unitarity, and negative norm states, revealing that the normalizable vacuum can be seen as spontaneous conformal symmetry breaking and presenting an interacting model that remains unitary.

Contribution

It offers a simplified discussion of ghosts and unitarity in the Pais-Uhlenbeck oscillator and introduces an interacting system that maintains unitarity despite coupling ghost and particle degrees of freedom.

Findings

Normalizable vacuum state as spontaneous conformal symmetry breaking

Existence of an interacting model that remains unitary

Clarification of ghost and unitarity issues in higher-derivative systems

Abstract

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.