{
  "id": "1907.11875",
  "version": "v1",
  "published": "2019-07-27T08:42:25.000Z",
  "updated": "2019-07-27T08:42:25.000Z",
  "title": "New approach to scalar products of Bethe vectors",
  "authors": [
    "A. Liashyk"
  ],
  "categories": [
    "math-ph",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "We consider quantum integrable models solvable by the algebraic Bethe ansatz and possessing $\\mathfrak{gl}(2)$-invariant $R$-matrix. We study the models of both periodic boundary conditions and boundary conditions based on reflection algebra. We present a new method to calculate the scalar products based on formula of an action of transfer matrix of a model onto Bethe vector. Using this method we identify some coefficient in the multiple action of the transfer matrix with the scalar product between on-shell and off-shell Bethe vectors. This allows us to find determinant representation of the scalar products in both types of boundary conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-27T08:42:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "scalar product",
      "transfer matrix",
      "periodic boundary conditions",
      "algebraic bethe ansatz",
      "off-shell bethe vectors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}