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.
Highlights
Understanding the nature of dark matter remains a major challenge at the intersections of astrophysics, cosmology, and particle physics
In this paper we have developed a self-consistent framework for obtaining an effective field theory to describe the nonrelativistic limit of a relativistic field theory
The lowestorder corrections to the ultranonrelativistic limit arise both from expanding the kinetic energy as well as from incorporating the backreaction from fast-oscillating terms on the dominant, slowly varying portion of the field
Summary
Understanding the nature of dark matter remains a major challenge at the intersections of astrophysics, cosmology, and particle physics. From the standpoint of particle theory, the puzzle of dark matter includes at least two components: identifying a plausible dark-matter candidate within realistic models of particle physics, and developing an accurate, theoretical description that is suitable for low-energy phenomena associated with cold matter For the latter goal, it is important to develop a means of characterizing the nonrelativistic limit of relativistic quantum field theories in a systematic way. We have in mind applications to axion dark matter [2,3,4,5], though the methods developed here should be applicable to the low-energy limits of other field theories, such as QED, QCD [6,7,8], and. The Lagrangian in Eq (4) has a global Uð1Þ symmetry; the associated conserved charge is the number of particles, Z
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