Effective Field Theories on the Jet Bundle

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.