On global behaviour of classical effective field theories

TL;DR

This paper rigorously analyzes classical effective field theories with one light and one heavy field, proving global existence, scattering, and an inverse mass expansion of solutions.

Contribution

It extends the mathematical understanding of classical EFTs by establishing global existence and scattering results in the high mass limit.

Findings

Global existence of solutions in the high mass limit

Solutions scatter linearly in the Lax-Philips sense

Final states admit an inverse mass expansion

Abstract

We continue the rigorous study of classical effective field theories (EFTs) that was recently initiated in the work of Reall and Warnick [RW22]. We study a system with one light and one heavy field with cubic coupling and prove global existence (of the UV solution) under an effective norm in the high mass limit. Furthermore, we prove that the global solution linearly scatters (in Lax-Philips sense) and that this final state has an expansion in inverse powers of the mass, and can be recovered from the EFT equation alone.