  We discuss a non-relativistic contraction of massive and massless field
theories minimally coupled to gravity. Using the non-relativistic limiting
procedure introduced in our previous work, we (re-)derive non-relativistic
field theories of massive and massless spins 0 to 3/2 coupled to torsionless
Newton-Cartan backgrounds. We elucidate the relativistic origin of the
Newton-Cartan central charge gauge field $m_\mu$ and explain its relation to
particle number conservation.
