Higher derivative theories with constraints : Exorcising Ostrogradski's Ghost

TL;DR

This paper demonstrates that the Ostrogradski instability in higher derivative theories can be eliminated only through the addition of constraints that reduce the phase space, addressing a fundamental issue in such theories.

Contribution

It provides a formal proof that constraints are necessary to remove Ostrogradski's ghost in non-degenerate higher derivative theories.

Findings

Ostrogradski instability can only be eliminated with phase space reduction.

Constraints are essential for stabilizing higher derivative theories.

Theoretical framework for handling higher derivative instabilities.

Abstract

We prove that the linear instability in a non-degenerate higher derivative theory, the Ostrogradski instability, can only be removed by the addition of constraints if the original theory's phase space is reduced.