Bethe-Salpeter equation: Spin-0-spin-½ and spin-0-spin-0 bound states

The Bethe-Salpeter equation is cast into a form in which the relationship between the relativistic quantum-mechanical two-body equation and the Bethe-Salpeter equation is established for a bound system whose constituents are either (i) a spinless particle and a particle of spin ½ or (ii) both particles spinless. The connection between these equations and their nonrelativistic counterpart is immediately apparent from these forms. To lay the groundwork for physical applications for such systems in which the Coulomb interaction is the main source of the binding, scalar quantum electrodynamics in the radiation gauge is developed. Using the foregoing, the perturbation theory for the Bethe-Salpeter equation is formulated for electromagnetic bound systems consisting of spinless particles and for systems for which the constituents are a spin-½ and a spinless particle, and its application to the exotic bound state is discussed. Included as well is a calculation of the ground-state energy to ${\alpha }^4\mathrm{th}$ order of an electromagnetically bound system which is comprised of a particle of spin 0 and one of spin ½.