INSTANTANEOUS BETHE–SALPETER EQUATION: IMPROVED ANALYTICAL SOLUTION

Abstract

Studying the Bethe–Salpeter formalism for interactions instantaneous in the rest-frame of the bound states described, we show that, for bound-state constituents of arbitrary masses, the mass of the ground state of a given spin may be calculated almost entirely analytically with high accuracy, without the (numerical) diagonalization of the matrix representation obtained by expansion of the solutions over a suitable set of basis states.