The Theorem of Ostrogradsky

TL;DR

This paper reviews Ostrogradsky's Hamiltonian formalism for higher derivative Lagrangians, highlighting the resulting instability that constrains fundamental field theories and discussing attempts to circumvent this issue.

Contribution

It provides a comprehensive review of Ostrogradsky's formalism and analyzes the implications of the instability for interacting field theories.

Findings

Ostrogradsky's construction leads to a fundamental instability in higher derivative theories.

This instability strongly restricts the development of consistent interacting field theories.

Attempts to evade the instability face significant theoretical challenges.

Abstract

Ostrogradsky's construction of a Hamiltonian formalism for nondegenerate higher derivative Lagrangians is reviewed. The resulting instability imposes by far the most powerful restriction on fundamental, interacting, continuum Lagrangian field theories. A discussion is given of the problems raised by attempts to evade this restriction.