Hirosuke Kuwabara

A time dependent Pais-Uhlenbeck oscillator and its decomposition

The Pais-Uhlenbeck(PU) oscillator is the simplest model with higher time derivatives, and its properties were studied for a long time.
In this paper, we extend the 4th order free PU oscillator to a non-trivial case, dubbed the 4th order time dependent PU(tdPU) oscillator, which has time dependent frequencies.
We show that this model cannot be decomposed into two harmonic oscillators in contrast to the original PU oscillator by a linear coordinate canonical transformation showed by Smilga. As a result of sustaining canonicality of this transformation for the tdPU oscillator, an interaction is added.