New (Ghost-Free) Formulation of the Pais-Uhlenbeck Oscillator

TL;DR

This paper introduces a novel, ghost-free formulation of the Pais-Uhlenbeck oscillator, a higher derivative model, by decomposing it into two harmonic oscillators, thereby resolving issues of unitarity and energy boundedness without complex transformations.

Contribution

The paper presents a new parametrization of the Pais-Uhlenbeck oscillator that eliminates unitarity and boundedness problems without using imaginary scaling or PT-symmetry.

Findings

Reproduces conventional results in one parametrization.

Eliminates unitarity and boundedness issues in another parametrization.

Avoids complex transformations like imaginary scaling or PT-symmetry.

Abstract

We provide a new formulation of the Pais-Uhlenbeck oscillator which is a prototype of a higher derivative model. Different parametrisations that reveal the model as a combination of two simple harmonic oscillators are introduced. Conventional results are reproduced in one realisation. In another, all problems related to lack of unitarity or boundedness of energy are eliminated since the hamiltonian is expressed as a sum of the hamiltonians of two decoupled harmonic oscillators. Recourse to imaginary scaling transformation or PT-symmetry, as advocated in the literature, are totally avoided.