Instantaneous Bethe–Salpeter Equation: Analytic Approach for Nonvanishing Masses of the Bound–State Constituents

The instantaneous Bethe–Salpeter equation, derived from the general Bethe–Salpeter formalism by assuming that the involved interaction kernel is instantaneous, represents the most promising framework for the description of hadrons as bound states of quarks from first quantum-field-theoretic principles, 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 an eigenvalue problem for an explicitly—more precisely, algebraically—known matrix, at least, for a rather wide class of interactions between these bound-state constituents. The advantages of the explicit knowledge of this matrix representation are self-evident. PACS numbers : 11.10.St, 03.65.Ge ∗ E-mail address : [email protected] ‡ E-mail address : [email protected] † E-mail address : [email protected]