Covariant two-body dynamics and the Weinberg equation

Covariant, constrained two-body dynamics, with both particles put on their mass shells, is proposed as a generalization of the Bakamjian-Thomas-Coester relativistic quantum-mechanical scheme. The Weinberg infinite-momentum limit of the latter scheme is investigated, and a covariant formulation of the two-body problem in the light-front field theory approach is made. We find several equivalent versions of the three-dimensional, covariant, two-body integral equations. Among these equations we get one in which the covariant two-body propagator has the form identical with the nonrelativistic case, i.e., we have a quadratic structure in the relative momentum and the ordinary reduced mass. We discuss connections between different schemes, emphasizing the variety and the uniqueness of the off-shell extensions