{
  "id": "1610.03463",
  "version": "v1",
  "published": "2016-10-11T18:48:01.000Z",
  "updated": "2016-10-11T18:48:01.000Z",
  "title": "The BV formalism: theory and application to a matrix model",
  "authors": [
    "Roberta A. Iseppi"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We review the BV formalism in the context of $0$-dimensional gauge theories. For a gauge theory $(X_{0}, S_{0})$ with an affine configuration space $X_{0}$, we describe an algorithm to construct a corresponding extended theory $(\\tilde{X}, \\tilde{S})$, obtained by introducing ghost and anti-ghost fields, with $\\tilde{S}$ a solution of the classical master equation in $\\mathcal{O}_{\\tilde{X}}$. This construction is the first step to define the (gauge-fixed) BRST cohomology complex associated to $(\\tilde{X}, \\tilde{S})$, which encodes many interesting information on the initial gauge theory $(X_{0}, S_{0})$. The second part of this article is devoted to the application of this method to a matrix model endowed with a $U(2)$-gauge symmetry, explicitly determining the corresponding $\\tilde{X}$ and the general solution $\\tilde{S}$ of the classical master equation for the model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-11T18:48:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bv formalism",
      "matrix model",
      "application",
      "classical master equation",
      "dimensional gauge theories"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}