dorsal/arxiv
View SchemaExact 1-Fermion Loop Contributions in 1+1 Dimensional Solitons
| Authors | J. R. Shepard, C. E. Price, T. C. Ferrée |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9212002 |
| URL | https://arxiv.org/abs/nucl-th/9212002 |
| DOI | 10.1103/PhysRevD.48.822 |
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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"abstract": "We find solutions to the 1+1 dimensional scalar-only linear sigma model. A\nnew method is used to compute 1-fermion loop contributions exactly and\nagreement with published results employing other methods is excellent. A\nrenormalization scheme which differs from that commonly used in such\ncalculations but similar to that required in 1+3 dimensions is also presented.\nWe compare ``kink\u0027\u0027 {\\it versus} ``shallow bag\u0027\u0027 solutions paying careful\nattention to the implications of the 1-fermion loop contributions for the\nstability of the former. We find that, for small fermion multiplicities,\nself-consistent shallow bag solutions are always more bound than their\nmetastable kink counterparts. However, as the fermion multiplicity increases,\nshallow bags evolve into kinks which eventually are the only self-consistent\nconfigurations. This situation is qualitatively the same for the two\nrenormalization schemes considered. When we construct ``baryons\u0027\u0027, each\ncontaining three fermions, the kink configuration is typically more bound than\nthe shallow bag when 1-fermion loop contributions are included.",
"arxiv_id": "nucl-th/9212002",
"authors": [
"J. R. Shepard",
"C. E. Price",
"T. C. Ferr\u00e9e"
],
"categories": [
"nucl-th"
],
"doi": "10.1103/PhysRevD.48.822",
"title": "Exact 1-Fermion Loop Contributions in 1+1 Dimensional Solitons",
"url": "https://arxiv.org/abs/nucl-th/9212002"
},
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