  A construction of the Coulomb-Breit Hamiltonian for a pair of fermions,
considered as a quantum two-body system, immersed in an arbitrary background
gravitational field described by Einstein's General Relativity is presented.
Working with Fermi normal coordinates for a freely falling observer in a
spacetime region where there are no background sources and ignoring the
gravitational back-reaction of the system, the effective Coulomb-Breit
Hamiltonian is obtained starting from the S-matrix element corresponding to the
one-photon exchange between the charged fermionic currents. The contributions
due to retardation are considered up to order (v/c)^2 and they are subsequently
written as effective operators in the relativistic quantum mechanical Hilbert
space of the system. The final Hamiltonian includes effects linear in the
curvature and up to order (v/c)^2.
