An alternative Hamiltonian formulation for the Pais-Uhlenbeck oscillator

TL;DR

This paper develops an alternative Hamiltonian formulation for the Pais-Uhlenbeck oscillator, addressing the unbounded Hamiltonian issue and extending the approach to supersymmetric cases, potentially improving quantum stability.

Contribution

It introduces a new Hamiltonian formulation for the Pais-Uhlenbeck oscillator that avoids the ghost problem and generalizes to supersymmetric versions.

Findings

Constructed an alternative Hamiltonian avoiding unboundedness.

Extended the formulation to supersymmetric oscillators.

Provided a framework for stable quantum descriptions.

Abstract

Ostrogradsky's method allows one to construct Hamiltonian formulation for a higher derivative system. An application of this approach to the Pais-Uhlenbeck oscillator yields the Hamiltonian which is unbounded from below. This leads to the ghost problem in quantum theory. In order to avoid this nasty feature, the technique previously developed in [Acta Phys. Polon. B 36 (2005) 2115] is used to construct an alternative Hamiltonian formulation for the multidimensional Pais-Uhlenbeck oscillator of arbitrary even order with distinct frequencies of oscillation. This construction is also generalized to the case of an N=2 supersymmetric Pais-Uhlenbeck oscillator.