On the three-dimensional reductions of the Bethe-Salpeter equation and their one-body limits (two-boson and boson-fermion cases)

We transform the Bethe-Salpeter equation for the two-boson and for the boson-fermion systems into equivalent Salpeter or Sazdjian equations, with a three-dimensional (3D) potential directly computable from a series of reducible and irreducible Feynman graphs. We compute the various one-body limits (in the boson-fermion case we compute the heavy boson and the heavy fermion limits). To be definite, we work in the QED framework, but we also consider the scalar bosons exchanges in the two-boson case. (author)