Poincaré gauge theory and Galilean covariance

Abstract

We analyse the Poincaré gauge structure proposed by D. Cangemi and R. Jackiw (CJ) (Ann. Phys. (N.Y.)225, 229), in association with general Lie algebras and, in particular, with Galilean symmetries. In this context, the CJ method is formulated as an embedding scheme of metric spaces, and aspects of Galilean covariance are then used to analyse: (i) the non-relativistic limits of the electromagnetic field; (ii) a Galilean counterpart of the CJ theory; (iii) geometrical common structures of Lorentzian and Galilean physics; and (iv) a covariant formalism for classical mechanics.