Constructing effective field theories via their harmonics

TL;DR

This paper introduces a novel harmonic analysis approach to constructing operator bases in effective field theories by analyzing the harmonic modes of the kinematic Grassmannian, facilitating a new perspective on EFT formulation.

Contribution

It establishes a connection between EFT operator bases and harmonic modes on the kinematic Grassmannian, providing explicit constructions for low mass dimension operators.

Findings

Harmonic modes correspond to EFT operators on the kinematic Grassmannian.

Recasting EFT construction as harmonic analysis offers new analytical tools.

Explicit low mass dimension EFT operators are constructed.

Abstract

We consider the construction of operator bases for massless, relativistic quantum field theories, and show this is equivalent to obtaining the harmonic modes of a physical manifold (the kinematic Grassmannian), upon which observables have support. This enables us to recast the approach of effective field theory (EFT) through the lens of harmonic analysis. We explicitly construct harmonics corresponding to low mass dimension EFT operators.