We investigate spin-and velocity-dependent contributions to the gravitational interparticle potential. The methodology adopted here is based on the expansion of the effective action in terms of form factors encoding quantum corrections. Restricting ourselves to corrections up to the level of the graviton propagator, we compute, in terms of general form factors, the nonrelativistic gravitational potential associated with the scattering of spin-0 and-1=2 particles. We discuss comparative aspects concerning different types of scattered particles and we also establish some comparisons with the case of electromagnetic potentials. Moreover, we apply our results to explicit examples of form factors based on nonperturbative approaches for quantum gravity. Finally, the cancellation of Newtonian singularity is analyzed in the presence of terms beyond the monopole-monopole sector.

Dimensionality aspects of non-minimal electromagnetic couplings are investigated. By means of the Foldy–Wouthuysen transformation, we attain (non-)relativistic interactions related to the non-minimal coupling in three-dimensional spacetime, for both the bosonic and fermionic fields. Next, we establish some comparisons and analyze particular situations in which the external electromagnetic fields are described either by Maxwell or Maxwell–Chern–Simons Electrodynamics. In addition, we consider the situation of a non-minimal coupling for the fermionic field in four dimensions, carry out its dimensional reduction to three dimensions and show that the three-dimensional scenario previously worked out can be recovered as a particular case. Finally, we discuss a number of structural aspects of both procedures.