Spinors in the self-dual Yang-Mills field in the Minkowski space

The Yang-Mills theory is considered, where the infrared catastrophe is evaded by introduction of a collective degree of freedom, covariant with respect to a topologically non-trivial gauge group. The collective motion of the fields is associated with a spontaneous breaking of the vacuum symmetry and vacuum fields with a finite action satisfying the self-duality equation in the Minkowski space. Solutions of the Dirac equations in the self-dual fields depending on an arbitrary function are obtained. Observables (charge, energy, spin) are calculated for spinors in the ''vacuum'' and a Hermitean Hamiltonian is obtained. The physical picture is consistent with a relativistic extension of the hadronic bag model