BETHE-SALPETER-EQUATION FOR SPIN-0-SPIN-1/2 AND SPIN-0-SPIN-0 BOUND-STATES - PERTURBATION-THEORY AND APPLICATIONS

Consideration is given to a recently introduced formalism of the Bethe-Salpeter equation for bound systems whose constituents are either (i) a spinless and a spin-1/2 particle or (ii) where both particles are spinless. In this formalism the positive and negative energy states of the scalar particles are treated symmetrically in a two-component representation while the fermions are treated as usual. For these systems, this two-component representation leads to an unambiguous interpretation of the non-relativistic limit of the Bethe-Salpeter equation as well as providing a wave equation for the corresponding relativistic two-body quantum mechanics problem. To find the appropriate interaction kernel, the Lagrangian corresponding to this representation is found and for the weak coupling case, such as quantum electrodynamics, it is used in developing the perturbation theory. As an illustration of the perturbation theory, it is verified that the expected lowest-order energy shifts for the 2S(1/2) 2P(1/2) and 2P(3/2) states for a spin-0-spin-1/2 system, are obtained. The relevance of these developments to the energy levels of kaonic hydrogen and similar systems is discussed.