Hamiltonian formulation of non-Abelian gauge fields and nonrelativistic bound states

Abstract

For fermions minimally coupled to non-Abelian gauge fields, first-order quantization in the radiation gauge is presented in which the validity of naive Ward identities simplifies the renormalization procedure. Then, successive Foldy-Wouthuysen transformations are used to determine the nonrelativistic Hamiltonian operator as well as its first relativistic correction. This operator expansion is verified to all orders of perturbation theory by an extension of the Appelquist-Carazzone decoupling theorem. Next, the Hamiltonian, which provides a systematic starting point for any nonrelativistic calculation, is used to cast the fermion-antifermion nonrelativistic bound-state kernel into a simple and compact form which is spin independent and serves as the basis of a perturbative analysis. Through two loops, calculation of the kernel reveals that a mass-independent static potential exists in the nonrelativistic limit only for singlet states of the gauge group. Higher-loop corrections, three-fermion bound states, and nonperturbative methods are also discussed.