NoninstantaneousO(vc)relativistic effects in bound states and a covariant Schrödinger equation

The noninstantaneous and nonlocal interactions which follow from Weinberg-type dynamics are found to produce $\frac{v}{c}$ relativistic corrections to potentials which are nonrelativistic limits of certain field-theoretic dynamics. Such corrections may be applicable in, for example, phenomenological models of charmonium. These interactions are driving terms in a covariant three-dimensional two-body integral equation derivable from field theory. For bound systems this equation is a fully covariant Schrödinger equation, with spacelike relative momentum and a proper angular resolution. We study this equation, including its systematic relativistic corrections, in various limits based on scalar-particle-exchange dynamics. We compare and contrast it to a related but different three-]dimensional equation derivable from field theory which represents an equal-time projection. We also comment on other approaches to the relation between relativistic and nonrelativistic dynamics.