Non-relativistic fields from arbitrary contracting backgrounds

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