  We study the symmetries of non-relativistic systems with an emphasis on
applications to the fractional quantum Hall effect. A source for the energy
current of a Galilean system is introduced and the non-relativistic
diffeomorphism invariance studied in previous work is enhanced to a full
spacetime symmetry, allowing us to derive a number of Ward identities. These
symmetries are smooth in the massless limit of the lowest Landau level. We
develop a formalism for Newton-Cartan geometry with torsion to write these Ward
identities in a covariant form. Previous results on the connection between Hall
viscosity and Hall conductivity are reproduced.
