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

Abstract

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 kjUj4 in two and three dimensions, and the non-linear Schr€odinger 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.