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Abstract

The procedure of null reduction provides a concrete way of constructing field
theories with Galilean invariance. We use this to examine Galilean gauge
theories, viz. Galilean electrodynamics and Yang-Mills theories in spacetime
dimensions 3 and 4. Different non-relativistic conformal symmetries arise in
these contexts: Schr{\"o}dinger symmetry in $d=3$ and Galilean conformal
symmetry in $d=4$. A canonical analysis further reveals that the symmetries
enhance to their infinite dimensional versions in phase space and pick up
central extensions. In addition, for the Abelian theory, we discuss
non-relativistic electro-magnetic duality in $d=3$ and its difference with the
$d=4$ version. We also mention some quantum aspects for both Abelian and
non-Abelian theories.