Fermion-field nontopological solitons

Abstract

The interaction between a scalar field and a set of n fermion fields in three space dimensions is investigated by decomposing the total Hamiltonian H into a sum of two terms: H = H/sub qcl/ + H/sub corr/, where H/sub qcl/ denotes the quasiclassical part and H/sub corr/ the quantum correction. General theorems are given for H/sub qcl/ concerning the existence of soliton solutions, the general properties of such solutions, and the condition under which the lowest energy state of H/sub qcl/ is a soliton solution, not the usual plane-wave solution. The effects of the quantum-correction term H/sub corr/ are examined. It is shown that the quasiclassical solution is a good approximation to the quantum solution over a wide range of the coupling constant. The approximation becomes very good when the fermion number N is large. Even for small N (2 or 3) and weak coupling, the quasiclassical solution remains a fairly good approximation. In the strong-coupling region and for arbitrary N, the quasiclassical approximation becomes again very good, at least when the fermions are nonrelativistic. The question whether the relativistic quantum field theory has a strong-coupling limit or not is not resolved.