  We present the quantum field description of Galilean electrodynamics
minimally coupled to massless Galilean fermion in (3 + 1) dimensions. At the
classical level, the Lagrangian is obtained as a null reduction of a
relativistic theory in one higher dimension. We use functional techniques to
develop the quantum field description of the theory. Quantum corrections to the
propagators and vertex are obtained upto first order and the theory is found to
be renormalizable to this order. The beta function of the theory is found to
grow linearly; the theory is not asymptotically free.
