The spinor strong interaction model recently proposed to account for the meson spectra is extended to include interaction with external gauge fields. An action integral is constructed and a restricted variational principle is employed to reproduce the earlier basic meson equations. In establishing U(1) gauge invariance, the so-called U(1) problem, the absence of pseudoscalar singlet mesons that do not decay strongly, is naturally resolved. SU(2) x U(1) or SO(3) gauge invariance leads to that pseudoscalar isodoublet or isotriplet mesons can generate masses of the gauge bosons without recourse to the unobserved Higgs bosons of the standard electroweak model. Thegauge boson masses relate to the linear confinement potential constant of pseudoscalar mesons. The spinor strong interaction model is quantized in a macroscopic approximation due to the finite size of mesons. Commutation relations and the rest frame Hamiltonian are obtained. In this frame, the relative energy of the quark and antiquark is shown to vanish.
