A non-perturbative approach to the instability of the vacuum in the presence of fermions

We discuss in detail the possibility that states of fermion number one, consisting of the scalar field in its ground state and the occupancy of the zero-momentum plane-wave one for the fermionic quantum, may be unstable to the formation of a kink—antikink pair each carrying a fermion number of one-half. As a matter of fact we restrict ourselves to a bidimensional model which considers the Φ4 theory coupled to fermions by means of a Yukawa term. In particular we take advantage of the well-known bosonization procedure so that the scalar—fermion system becomes in the sequel a pure scalar model. Eventually we consider non-perturbative methods on the lattice, thus going beyond the classical treatments used by other authors.