Non-Abelian Gauge Fields and Nonrelativistic Bound States

The second-quantized Coulomb-gauge Hamiltonian for any nonrelativistic system of fermions minimally coupled to non-Abelian gauge fields is derived by performing successive non-Abelian Foldy-Wouthuysen transformations. In this general formalism, a detailed analysis is made of threshold fermion-antifermion bound states in the weak-coupling limit and the form of the two-loop nonrelativistic Bethe-Salpeter kernel is determined. This kernel gives a static potential independent of the fermion mass, but only for singlet states of the gauge group.