Relativistic Corrections to Nonrelativistic Effective 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.
Keywords
Cite
@article{arxiv.1712.00445,
title = {Relativistic Corrections to Nonrelativistic Effective Field Theories},
author = {Mohammad Hossein Namjoo and Alan H. Guth and David I. Kaiser},
journal= {arXiv preprint arXiv:1712.00445},
year = {2018}
}
Comments
31pp. References added, and 3 appendices added, showing (a) how to implement the field redefinition as a canonical transformation, (b) how to develop the effective field theory using a local field redefinition, and (c) how to use a further field redefinition to compare our results with those of Mukaida, Takimoto, and Yamada