{
  "id": "2203.15997",
  "version": "v1",
  "published": "2022-03-30T02:12:00.000Z",
  "updated": "2022-03-30T02:12:00.000Z",
  "title": "Quillen-type bundle and geometric prequantization on moduli space of the Seiberg-Witten equations on product of Riemann surfaces",
  "authors": [
    "Rukmini Dey"
  ],
  "comment": "6pages",
  "categories": [
    "math-ph",
    "math.DG",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "We show the existence of a symplectic structure on the moduli space of the Seiberg-Witten equations on $\\Sigma \\times \\Sigma$ where $\\Sigma$ is a compact oriented Riemann surface. To prequantize the moduli space, we construct a Quillen-type determinant line bundle on it and show its curvature is proportional to the symplectic form.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-30T02:12:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "moduli space",
      "seiberg-witten equations",
      "geometric prequantization",
      "quillen-type bundle",
      "quillen-type determinant line bundle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}