TL;DR
This paper develops an N=2 supersymmetric version of the Pais-Uhlenbeck oscillator, explores its symmetries, and analyzes its quantum properties, revealing issues like negative norm states and unbounded energy spectrum.
Contribution
It introduces a novel N=2 supersymmetric extension of the Pais-Uhlenbeck oscillator and examines its symmetry structure and quantum characteristics.
Findings
Quantum model contains negative norm states
Energy spectrum is unbounded from below
Symmetries of the supersymmetric oscillator are detailed
Abstract
We construct an N=2 supersymmetric extension of the Pais-Uhlenbeck oscillator for distinct frequencies of oscillation. A link to a set of decoupled N=2 supersymmetric harmonic oscillators with alternating sign in the Hamiltonian is introduced. Symmetries of the model are discussed in detail. The investigation of a quantum counterpart of the constructed model shows that the corresponding Fock space contains negative norm states and the energy spectrum of the system is unbounded from below.
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