Higher-Derivative Boson Field Theories and Constrained Second-Order Theories

TL;DR

This paper presents a novel covariant method to reduce higher-derivative relativistic field theories to second-order form using Lagrange multipliers, improving upon Ostrogradski's approach and applicable to various theories.

Contribution

It introduces a covariant two-derivative formulation for higher-derivative field theories, enabling easier analysis and generalization compared to traditional Ostrogradski methods.

Findings

Successfully applied to scalar models, generalized electrodynamics, and higher-derivative gravity.

Maintains explicit Lorentz invariance despite initial non-covariance in the procedure.

Offers a more suitable approach for extending to 2n-derivative theories.

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. Despite the intrinsic non-covariance of the Dirac's procedure used to deal with the constraints, the explicit Lorentz invariance is recovered at the end. We develop this new setting on the grounds of a simple scalar model and then its applications to generalized electrodynamics and higher-derivative gravity are worked out. For a wide class of field theories this method is better suited than Ostrogradski's for a generalization to 2n-derivative theories