Exact one-fermion-loop contributions in (1+1)-dimensional solitons.

We find solutions to the (1+1)-dimensional scalar-only linear [sigma] model. A new method is used to compute one-fermion-loop contributions exactly, and agreemment with published results employing other methods is excellent. A renormalization scheme which differs from that commonly used in such calculations but is similar to that required in 1+3 dimensions is also presented. We compare kink'' versus shallow bag'' solutions, paying careful attention to the implications of the one-fermion-loop contributions for the stability of the former. We find that, for small fermion multiplicities, self-consistent shallow bag solutions are always more bound than their metastable kink counterparts. However, as the fermion multiplicity increases, shallow bags evolve into kinks which eventually are the only self-consistent configurations. This situation is qualitatively the same for the two renormalization schemes considered. When we construct baryons,'' each containing three fermions, the kink configuration is typically more bound than the shallow bag when one-fermion-loop contributions are included.