Energy and stability of Pais-Uhlenbeck oscillator

TL;DR

This paper investigates the stability of higher-derivative systems, specifically the Pais-Uhlenbeck oscillator, using the Lagrange anchor framework to connect symmetries and conserved quantities for ensuring classical and quantum stability.

Contribution

It introduces a novel approach linking the Lagrange anchor with conserved quantities to analyze stability in higher-derivative models.

Findings

Classical and quantum stability depend on a bounded integral of motion.

A bounded integral of motion related to time translation ensures stability.

The Lagrange anchor effectively connects symmetries with conserved quantities.

Abstract

We study stability of higher-derivative dynamics from the viewpoint of more general correspondence between symmetries and conservation laws established by the Lagrange anchor. We show that classical and quantum stability may be provided if a higher-derivative model admits a bounded from below integral of motion and the Lagrange anchor that relates this integral to the time translation.