  Motivated by recent discussions of fractons, we explore nonrelativistic field
theories with a continuous global symmetry, whose charge is a spatial vector.
We present several such symmetries and demonstrate them in concrete examples.
They differ by the equations their Noether currents satisfy. Simple cases,
other than the translation symmetry, are an ordinary (relativistic) one-form
global symmetry and its nonrelativistic generalization. In the latter case the
conserved charge is associated with a codimension-one spatial manifold, but it
is not topological. More general examples involve charges that are integrated
over the entire space. We also discuss the coupling of these systems to gauge
fields for these symmetries. We relate our examples to known continuum and
lattice constructions.
