Classical solution of the equations of motion in the quantum theory of Fermi fields

A study is made of the behavior of a quantum-field Fermi–Bose system in the neighborhood of a classical solution of the equations of motion that contains both a boson and a spinor component with the latter being treated as a Grassmann background component of the fermion field. The conditions under which such an interpretation of a classical spinor field is possible is made. It is shown that when these conditions are satisfied such a component describes a phase with spontaneously broken charge symmetry and elements of dynamical supersymmetry.