Ostrogradski Formalism for Higher-Derivative Scalar Field Theories

TL;DR

This paper extends the Ostrogradski formalism to higher-derivative scalar field theories, providing a covariant, phase-space validated method that clarifies the roles of physical and ghost fields, with implications for higher-derivative gravity.

Contribution

It develops a covariant Ostrogradski approach for higher-derivative relativistic scalar fields, including phase-space analysis and explicit identification of physical and ghost degrees of freedom.

Findings

The formalism reduces higher-derivative Lagrangians to second order.

Explicit separation of physical and ghost fields is achieved.

Results support covariant methods in higher-derivative gravity.

Abstract

We carry out the extension of the Ostrogradski method to relativistic field theories. Higher-derivative Lagrangians reduce to second differential-order with one explicit independent field for each degree of freedom. We consider a higher-derivative relativistic theory of a scalar field and validate a powerful order-reducing covariant procedure by a rigorous phase-space analysis. The physical and ghost fields appear explicitly. Our results strongly support the formal covariant methods used in higher-derivative gravity.