Flux-tube model, quark-antiquark potential, and Bethe-Salpeter kernel

We reconsider the problem of the quantization of the relativistic flux-tube model already treated in the literature and show how to make it completely consistent with the effective quark-antiquark Hamiltonian derived from QCD in the context of the Wilson loop approach. We obtain an explicit form for the model Hamiltonian as an expansion in the string tension constant and construct an instantaneous related Bethe-Salpeter kernel including even the spin and the short-range part of the interaction.