In QED, one can relate the two-particle scattering amplitude to a static potential in the non-relativistic limit using the Born approximation. E.g. in Peskin and Schroeder pg. 125, the tree-level scattering amplitude for electron-electron scattering is computed, and in the non-relativistic limit one finds the Coulomb potential. If one allows for 1/c^2 effects in the non-relativistic expansion, one also finds spin-dependent interactions (e.g. spin-orbit, see Berestetskii, Lifshitz, Pitaevskii pg. 337).
Are there any alternative methods for calculating a two-particle non-relativistic potential?