Effective Field Theories on the Jet Bundle

TL;DR

This paper introduces a covariant geometric framework on jet bundles for higher-derivative scalar field theories, simplifying the analysis of scattering amplitudes and invariance properties.

Contribution

It develops a generalized field space geometry on jet bundles that accounts for higher derivatives and maintains invariance under field redefinitions and total derivatives.

Findings

Formulation of a jet bundle analog to the field space metric.

Demonstration of invariance of amplitude contributions under total derivatives.

Extension of covariant geometry to higher-derivative theories.

Abstract

We develop a generalized field space geometry for higher-derivative scalar field theories, expressing scattering amplitudes in terms of a covariant geometry on the all-order jet bundle. The incorporation of spacetime and field derivative coordinates solves complications due to higher-order derivatives faced by existing approaches to field space geometry. We identify a jet bundle analog to the field space metric that, besides field redefinitions, exhibits invariance under total derivatives. The invariance consequently extends to its amplitude contributions and the canonical covariant geometry.