Enlarged NH symmetries: Particle Dynamics and Gauge Symmetries

TL;DR

This paper explores how Newton-Hooke symmetries can be extended with additional translation vectors, leading to new particle dynamics and gauge invariances, especially in lower dimensions.

Contribution

It introduces an enlarged NH symmetry group with new translation vectors, classifies its central extensions, and derives the most general invariant particle dynamics.

Findings

Enlarged NH symmetries include additional translation vectors.

Central extensions depend on parameters and dimensions.

Gauge invariances simplify dynamics to standard NH form.

Abstract

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