Pais–Uhlenbeck oscillator and negative energies

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 below and above. We review some approaches in the literature that attempt to avoid the problem of negative energies in the Pais–Uhlenbeck oscillator.