  We study the classical and quantum "properties" of Galilean fermions in 3+1
dimensions. We have taken the case of massless Galilean fermions minimally
coupled to the scalar field. At the classical level, the Lagrangian is obtained
by null reducing the relativistic theory in one higher dimension. The resulting
theory is found to be invariant under infinite Galilean conformal symmetries.
Using Noether's procedure, we construct the corresponding infinite conserved
charges. Path integral techniques are then employed to probe the quantum
"properties" of the theory. The theory is found to be renormalizable. A novel
feature of the theory is the emergence of mass scale at the first order of
quantum correction. The conformal symmetry of the theory breaks at the quantum
level. We confirm this by constructing the beta function of the theory.
