{
  "id": "2405.10549",
  "version": "v1",
  "published": "2024-05-17T05:27:26.000Z",
  "updated": "2024-05-17T05:27:26.000Z",
  "title": "Spectral energy of Dirac operators for fermion scattering on topological solitons in the nonlinear $O(3)$ $σ$-model",
  "authors": [
    "Daiju Funakawa",
    "Satoshi Okumura",
    "Yuki Ueda"
  ],
  "comment": "12 pages",
  "categories": [
    "math-ph",
    "math.FA",
    "math.MP"
  ],
  "abstract": "We present a criteria affirming the existence of discrete ground states of the Dirac operators which describe the fermion scattering on topological solitons in the nonlinear $O(3)$ $\\sigma$-model. Additionally, we investigate a sufficient condition that elucidates the phenomenon of supersymmetry breaking within the supersymmetric quantum mechanics associated with this Dirac operator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-17T05:27:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q10",
      "47A75",
      "47B25",
      "81Q60"
    ],
    "keywords": [
      "dirac operator",
      "topological solitons",
      "fermion scattering",
      "spectral energy",
      "discrete ground states"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}