Higher-derivative scalar field theories as constrained second-order theories

TL;DR

This paper introduces a new method to reformulate higher-derivative scalar field theories as second-order theories using covariant two-derivative formulations with Lagrange multipliers, preserving Lorentz invariance.

Contribution

It presents an alternative to Ostrogradski's method by directly rewriting higher-derivative theories as second-order covariant theories with new fields and constraints.

Findings

Successfully applied to a simple scalar model

Outlined applications to generalized electrodynamics

Discussed extension to higher-derivative gravity

Abstract

As an alternative to the covariant Ostrogradski method, we show that higher-derivative relativistic Lagrangian field theories can be reduced to second differential-order by writing them directly as covariant two-derivative theories involving Lagrange multipliers and new fields. Notwithstanding the intrinsic non-covariance of the Dirac's procedure used to deal with the constraints, the Lorentz invariance is recovered at the end. We develope this new setting for a simple scalar model and then its applications to generalized electrodynamics and higher-derivative gravity are outlined. This method is better suited than Ostrogradski's for a generalization to 2n-derivative theories.