No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model

TL;DR

A new realization of the fourth-order derivative Pais-Uhlenbeck oscillator is constructed that possesses no states of negative norm and has a real energy spectrum that is bounded below.

Abstract

Contrary to common belief, it is shown that theories whose field equations are higher than second order in derivatives need not be stricken with ghosts. In particular, the prototypical fourth-order derivative Pais-Uhlenbeck oscillator model is shown to be free of states of negative energy or negative norm. When correctly formulated (as a $\cP\cT$ symmetric theory), the theory determines its own Hilbert space and associated positive-definite inner product. In this Hilbert space the model is found to be a fully acceptable quantum-mechanical theory that exhibits unitary time evolution.