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.

Formation, gravitational clustering, and interactions of nonrelativistic solitons in an expanding universe

“…This completes our derivation, with caveats, of the master equations (1) that are used in the main body of the paper. For recent derivations and discussions of the non-relativistic limit, as well as decay rates for solitons with and without weak-field gravity (but in a non-expanding universe), see [49,50].…”

Global view of QCD axion stars

“…A potential downside of the GRB formalism is that gravity has not been included. Other methods for determining relativistic corrections in real scalar field theory suffer from a similar limitation [36,47,48] (though see [49] for some preliminary steps in this direction). Indeed, for the purposes of this section (describing the crossover from transition to dense branches of solutions), this does not constitute a serious limitation, as gravity is completely negligible over that range of solutions.…”

“…In Figure 2, we show ∆ (middle panel) and the chemical potential µ (bottom panel) as functions of the central field value Z(0); clearly, as Z(0) grows, the nonrelativistic GPP approach becomes increasingly suspect, and once Z(0) 10, one expects extremely large relativistic corrections. A recent work has formulated a perturbative method to take relativistic corrections into account using a GPP-like formalism [47]; for a φ 4 potential, the results are equivalent to those of the GRB method described in Section III A 2.…”

Non-relativistic reduction of spinors, new currents and their algebra

“…A possible way is to abstract the NR limit of the corresponding relativistic theory by developing a systematic algorithm. This approach has found applications in various contexts; for example, in fluid dynamics [1,2], in identifying possible dark matter candidates in particle physics models [3,4], understanding NR diffeomorphism [5,6,7] and other assorted phenomena [8,9,10].…”

“…Then the passage to the Schrodinger theory may be achieved [9]. There is a reasonable amount of literature [7,4,9] in discussing the transition of the scalar theory to the Schrodinger theory, both in flat and curved backgrounds.…”