Non-relativistic scale anomalies

We extend the cohomological analysis in arxiv:1410.5831 of anisotropic lifshitz scale anomalies. we consider non-relativistic theories with a dynamical critical exponent z = 2 with or without non-relativistic boosts and a particle number symmetry. we distinguish between cases depending on whether the time direction does or does not induce a foliation structure. we analyse both 1 + 1 and 2 + 1 spacetime dimensions. in 1 + 1 dimensions we find no scale anomalies with galilean boost symmetries. the anomalies in 2 + 1 dimensions with galilean boosts and a foliation structure are all b-type and are identical to the lifshitz case in the purely spatial sector. with galilean boosts and without a foliation structure we find also an a-type scale anomaly. there is an infinite ladder of b-type anomalies in the absence of a foliation structure with or without galilean boosts. we discuss the relation between the existence of a foliation structure and the causality of the field theory.