Jet Bundle Geometry of Scalar Field Theories

• Mohammad Alminawi

A geometric description of EFTs where the 2-derivative term is obtained by pulling back a metric from a manifold $M$ to spacetime $\Sigma$ has long been established. We introduce the concept of using geometry of fiber bundles $(\pi:E \to \Sigma)$ and in particular jet bundles $(\pi_1: J^1E \to \Sigma)$ where the scalar field becomes a section of the bundle to capture the potential and higher derivative terms in the metric. Field redefinitions, symmetries and the connection to amplitudes are examined in the context of the 1-jet bundle describing a Lagrangian up to 4 derivatives.

Effective Field Theories on the Jet Bundle

• Alan Lee

Field-redefinition invariant properties of EFTs, such as scattering amplitudes, can be captured via geometric techniques. However, the conventional Riemannian field space framework is inapplicable to higher-derivative theories. In this talk, I will discuss how the field space geometry can be extended to the jet bundle for scalar theories, in a manner that exhibits invariance under field redefinitions and total derivatives. This jet bundle geometry accommodates field derivatives of any order and constitutes a minimal complete framework for describing invariant EFT physics.

On Amplitudes and Field Redefinitions

• Xiaochuan Lu (University of California, San Diego)

Field redefinitions are responsible for many complications in the EFT formalism. Taming field redefinitions can help us stay away from these subtleties and facilitate the calculations. Non-derivative field redefinitions are better understood from geometric pictures, such as field space geometry and jet bundle geometry. On the other hand, derivative field redefinitions are more challenging. In this talk, I discuss a new angle of studying derivative field redefinitions. Following the same spirit of functional matching calculations, we track the change of the 1PI Effective Action under general field redefinitions. We identify a class of 1PI Effective Action transformations that would guarantee the invariance of on-shell amplitudes. This result serves as a lemma for better understanding derivative field redefinitions, and seeking an elegant geometric picture for them.