{
  "annotation_id": "0e381f23-4c79-4724-96dc-e9120d314208",
  "date_created": "2026-03-02T18:01:21.793000Z",
  "date_modified": "2026-03-02T18:01:21.793000Z",
  "file_hash": "c14d2e2d7567ad3309c24a304671aebcf9f6b79b3d5082e4217e9aa2b54342a0",
  "private": false,
  "record": {
    "abstract": "In previous report (J. Phys. A (1997) 30 4019-4029), I showed that the Dirac\nfield confined in a surface immersed in $R^3$ by means of a mass type potential\nis governed by the Konopelchenko-Kenmotsu-Weierstrass-Enneper equation. In this\narticle, I quantized the Dirac field and calculated the gauge transformation\nwhich exhibits the gauge freedom of the parameterization of the surface. Then\nusing the Ward-Takahashi identity, I showed that the expectation value of the\naction of the Dirac field is expressed by the Willmore functional and area of\nthe surface.",
    "arxiv_id": "physics/9707010",
    "authors": [
      "Shigeki Matsutani"
    ],
    "categories": [
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1142/S0129055X99000076",
    "journal_ref": "Rev.Math.Phys.11:171-186,1999",
    "title": "Immersion Anomaly of Dirac Operator on Surface in R^3",
    "url": "https://arxiv.org/abs/physics/9707010"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "183f3594-675a-45fd-854e-48fd48ff032f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}