Three-dimensional covariant formulation of the two-body problem in quantum field theory

The relativistic two-body problem is considered in an arbitrary frame of reference on the basis of the three-dimensional formulation of quantum field theory. Relative momenta are introduced by means of an addition operation in Lobachevskii space; it is shown the center of mass motion can then be separated and the problem formulated in a single-particle form. This makes it possible to formulate the quasipotential approach in a covariant form mad introduce a relativistic configuration space. This approach is compared with the analogous formulation of the nonrelativistic problem.