Galilean conformal mechanics from nonlinear realizations

Abstract

We apply the nonlinear realizations method for constructing new Galilean conformal mechanics models. Our starting point is the Galilean conformal algebra which is a nonrelativistic contraction of its relativistic counterpart. We calculate Maurer-Cartan one-forms, examine various choices of the relevant coset spaces, and consider the geometric inverse Higgs-type constraints which reduce the number of the independent coset parameters and, in some cases, provide dynamical equations. New Galilean conformally invariant actions are derived in arbitrary space-time dimension $D=d+1$ (no central charges), as well as in the special dimension $D=2+1$ with one exotic central charge. We obtain new classical mechanics models which extend the standard ($D=0+1$) conformal mechanics in the presence of $d$ nonvanishing space dimensions.