From self-consistent covariant effective field theories to their Galilean-invariant counterparts

TL;DR

This paper explores how to derive Galilean-invariant nonrelativistic limits from relativistic effective field theories, emphasizing the importance of second-order terms for accurate physical effects like spin-orbit coupling.

Contribution

It introduces a modified mapping procedure to obtain Galilean invariance beyond first order, improving the nonrelativistic limit of relativistic theories.

Findings

Standard v/c expansion yields only first-order Galilean invariance.

Second-order terms are crucial for effects like spin-orbit force.

Proposed mapping method better captures nonrelativistic limits.

Abstract

We discuss how to obtain the nonrelativistic limit of a self-consistent relativistic effective field theory for dynamic problems. It is shown that the standard v/c expansions yields Galilean invariance only to first order in v/c, whereas second order is required to obtain important contributions such as the spin-orbit force. We propose a modified procedure which is a mapping rather than a strict v/c expansion.