Pais-Uhlenbeck Oscillator and Negative Energies

TL;DR

This paper reviews negative energies in the Pais-Uhlenbeck oscillator, highlighting their non-problematic nature without interactions and the instability issues introduced by interactions coupling positive and negative energies.

Contribution

It clarifies conditions under which negative energies are harmless and reviews literature approaches to mitigate their problematic effects in the oscillator.

Findings

Negative energies are not problematic without interactions.

Interactions coupling positive and negative energies cause instability.

Bounded potentials can prevent system instability.

Abstract

We review the occurrence of negative energies in Pais-Uhlenbeck oscillator. We point out that in the absence of interactions negative energies are not problematic, neither in the classical nor in the quantized theory. However, in the presence of interactions that couple positive and negative energy degrees of freedom the system is unstable, unless the potential is bounded from bellow and above. We review some approaches in the literature that attempt to avoid the problem of negative energies in the Pais-Uhlenbeck oscillator.