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Exact 1-Fermion Loop Contributions in 1+1 Dimensional Solitons

J. R. Shepard·C. E. Price·T. C. Ferrée
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Abstract

We find solutions to the 1+1 dimensional scalar-only linear sigma model. A new method is used to compute 1-fermion loop contributions exactly and agreement with published results employing other methods is excellent. A renormalization scheme which differs from that commonly used in such calculations but similar to that required in 1+3 dimensions is also presented. We compare ``kink'' {\it versus} ``shallow bag'' solutions paying careful attention to the implications of the 1-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 1-fermion loop contributions are included.

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J. R. Shepard, C. E. Price, T. C. Ferrée. 1992-12-07. Exact 1-Fermion Loop Contributions in 1+1 Dimensional Solitons. https://doi.org/10.1103/physrevd.48.822

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