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: Schrödinger 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.
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