Enlarged NH symmetries: Particle dynamics and gauge symmetries

摘要

We show how the Newton–Hooke (NH) symmetries, representing a nonrelativistic version of de-Sittersymmetries, can be enlarged by a pair of translation vectors describing in Galilean limit the class ofaccelerations linear in time. We study the Cartan–Maurer one-forms corresponding to such enlargedNH symmetry group and by using cohomological methods we determine the general 2-parameter (inD = 2 + 1 4-parameter) central extension of the corresponding Lie algebra. We derive by using nonlinearrealizations method the most general group—invariant particle dynamics depending on two (inD = 2+1 on four) central charges occurring as the Lagrangean parameters. Due to the presence of gaugeinvariances we show that for the enlarged NH symmetries quasicovariant dynamics reduces to the onefollowing from standard NH symmetries, with one central charge in arbitrary dimension D and withsecond exotic central charge in D = 2+1.