The Ostrogradsky instability can be overcome by quantum physics

TL;DR

This paper explores how quantum physics can potentially resolve the classical Ostrogradsky instability in higher derivative theories, challenging traditional Hamiltonian analysis predictions.

Contribution

It demonstrates through a simple model that quantum effects can circumvent the classical Ostrogradsky instability in higher derivative theories.

Findings

Quantum treatment can avoid Ostrogradsky instability

Classical Hamiltonian analysis does not always predict quantum behavior

Simple model illustrates the potential for stability in quantum regimes

Abstract

In theories with higher time derivatives, the Hamiltonian analysis of Ostrogradsky predicts an instability. However, this Hamiltonian treatment does not correspond the way that these theories are treated in quantum field theory, and the instability may be avoided in at least some cases. We present a very simple model which illustrates these features.