Lorentz-like formulation of Galilean field theories

We review recent articles in which we have constructed nonrelativistic Lagrangian field models by enforcing Galilean covariance on a (4,1) Minkowski manifold and by reducing onto the (3,1) Newtonian space-time. This formalism provides an elegant construction of nonrelativistic Lagrangians, for example, those that describe the electric and magnetic limits of Galilean electromagnetism. We discuss the quantization of scalar and Fermi fields. Scattering amplitudes and cross sections are computed for the Coulomb interaction, as well as electron-electron and electron-positron scattering.