{
  "id": "cond-mat/0702223",
  "version": "v4",
  "published": "2007-02-08T20:45:41.000Z",
  "updated": "2007-08-26T10:00:11.000Z",
  "title": "Coherent state path integral and super-symmetry for condensates composed of bosonic and fermionic atoms",
  "authors": [
    "Bernhard Mieck"
  ],
  "journal": "Fortschr. Phys. (\"Progress of Physics\") Vol. 55, (No. 9-10), pp. 989-1120 (2007)",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "A super-symmetric coherent state path integral on the Keldysh time contour is considered for bosonic and fermionic atoms which interact among each other with a common short-ranged two-body potential. We investigate the symmetries of Bose-Einstein condensation for the equivalent bosonic and fermionic constituents and specialize on the examination of super-symmetries for pair condensate terms. A Hubbard-Stratonovich transformation from 'Nambu'-doubled super-fields leads to a generating function with super-matrices for the self-energy whose manifold is given by the ortho-symplectic super-group Osp(S,S|2L). Effective equations are derived for anomalous terms which are related to the molecular- and BCS- condensate pairs. A change of integration measure for the coset decomposition Osp(S,S|2L)/U(L|S)xU(L|S) is performed, including a separation of density and anomalous parts of the self-energy with a gradient expansion for the Goldstone modes. The independent anomalous fields in the actions can be transformed by the inverse square root of the metric tensor of Osp(S,S|2L)/U(L|S) so that the coset integration measure with the super-Jacobi-determinant can be removed from the coherent state path integral and Gaussian-like integrations remain. The variations of the independent coset fields in the effective actions result in classical field equations for a nonlinear sigma model with the anomalous terms.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2007-08-26T10:00:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fermionic atoms",
      "condensates",
      "super-symmetry",
      "super-symmetric coherent state path integral",
      "integration measure"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1002/prop.200710392",
      "journal": "Fortschritte der Physik",
      "year": 2007,
      "month": "Sep",
      "volume": 55,
      "number": "9-10",
      "pages": 989
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007ForPh..55..989M"
    }
  }
}