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

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.

6 pages; expanded version with additional references