Relativistic Corrections to Nonrelativistic Effective Field Theories

TL;DR

This paper introduces a systematic formalism for deriving nonrelativistic effective theories from relativistic scalar fields, including relativistic corrections, with potential applications in axion dark matter research.

Contribution

It develops a novel nonlocal field redefinition method to obtain low-energy effective theories with relativistic corrections from relativistic scalar fields.

Findings

Incorporates relativistic kinetic energy corrections.

Models backreaction of fast oscillations on slow field dynamics.

Applicable to axion dark matter and other field theories.

Abstract

In this paper we develop a formalism for studying the nonrelativistic limit of relativistic field theories in a systematic way. By introducing a simple, nonlocal field redefinition, we transform a given relativistic theory, describing a real, self-interacting scalar field, into an equivalent theory, describing a complex scalar field that encodes at each time both the original field and its conjugate momentum. Our low-energy effective theory incorporates relativistic corrections to the kinetic energy as well as the backreaction of fast-oscillating terms on the behavior of the dominant, slowly varying component of the field. Possible applications of our new approach include axion dark matter, though the methods developed here should be applicable to the low-energy limits of other field theories as well.