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

TL;DR

This paper demonstrates that the fourth-order Pais-Uhlenbeck oscillator model, when properly formulated as a PT-symmetric theory, is free of ghosts and maintains unitarity, challenging the belief that higher-order theories are inherently problematic.

Contribution

It proves the ghost-free nature of the fourth-order Pais-Uhlenbeck oscillator within a PT-symmetric framework, establishing its viability as a consistent quantum theory.

Findings

The model is free of negative energy states.

The theory admits a positive-definite inner product.

It exhibits unitary time evolution.

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.