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 Phi(4) 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. [References: 16]
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