Galilei-covariant path-integral quantization of non-relativistic complex scalar fields

We consider the functional quantization of non-relativistic theories of complex scalar fields with Galilean covariance. We define the generating functionals and the Green's functions by utilizing the five-dimensional prescription of Galilean covariance. As an example, we consider the self-interacting scalar field with coupling term λ|PHI|4 in two and three dimensions, and the non-linear Schroedinger equation, having in mind applications to the phenomenon of Bose-Einstein condensation. Our calculations of scattering amplitudes in two dimensions agree with results found in the literature