Instantaneous Bethe-Salpeter equation: Analytic approach for nonvanishing masses of the bound-state constituents - art. no. 036007

The instantaneous Bethe-Salpeter equation, derived from the general Bethe-S alpeter formalism by assuming that the involved interaction kernel is insta ntaneous, represents the most promising framework for the description of ha drons as bound states of quarks from first quantum-field-theoretic principl es, that is, quantum chromodynamics. Here, by extending a previous analysis confined to the case of bound-state constituents with vanishing masses, we demonstrate that the instantaneous Bethe-Salpeter equation for bound-state constituents with (definitely) nonvanishing masses may be converted into a n eigenvalue problem for an explicitly-more precisely, algebraic ally-known matrix, at least, for a rather wide class of interactions between these bo und-state constituents. The advantages of the explicit knowledge of this ma trix representation are self-evident.