Non-relativistic limit for Higher Spin Fields and Planar Schroedinger Equation in 3D

Abstract

Higher spin (HS) fields naturally occur in string theory, they are considered as a candidate for dark matter and may also appear as a collective excitation in condensed matter systems. In some cases one may study the HS fields in the non-relativistic settings. Thus, it is of interest to know the non-relativistic limit of HS fields and how to find the Schroedinger equation as the dynamical equation in this limit. In this paper, we consider the non-relativistic limit of HS fields in Minkowskian spacetime in 3D. We work both at the level of equation of motion and action/Lagrangian density. We find the systematic procedures in both settings and show that they can be generalized to arbitrary HS fields.