Low-Energy Theorem for Scalar and Vector Interactions of a Composite Spin-½ System

Scalar and vector interactions, with the scalar interaction coupled to a composite spin-½ system so as to cause a shift of its mass, are shown to obey a low-energy theorem which guarantees that the second order interaction due to $Z$ graphs is the same as for a point Dirac particle. Off-shell and contact interactions appropriate to the composite system cancel, and this is verified in a model of a composite fermion. The result suggests a justification for the use of the Dirac equation as it has been used in relativistic nuclear scattering and mean field theories.