The Lichnerowicz-Weitzenboeck formula and superconductivity
- Departamento de Fisica dos Solidos, Universidade Federal do Rio de Janeiro, 21941-972 Rio de Janeiro (Brazil)
- Centro Brasileiro de Pesquisas Fisicas, 22290-160 Rio de Janeiro RJ (Brazil)
We derive the Lichnerowicz-Weitzenboeck formula for the two-component order parameter superconductor, which provides a twofold view of the kinetic energy of the superconductor. For the one component order parameter superconductor we review the connection between the Lichnerowicz-Weitzenboeck formula and the Ginzburg-Landau theory. For the two-component case we claim that this formula opens a venue to describe inhomogeneous superconducting states intertwined by spin correlations and charged dislocation. In this case the Lichnerowicz-Weitzenboeck formula displays local rotational and electromagnetic gauge symmetry (SU(2) Circled-Times U(1)) and relies on local commuting momentum and spin operators. The order parameter lives in a space with curvature and torsion described by Elie Cartan geometrical formalism. The Lichnerowickz-Weitzenboeck formula leads to first order differential equations that are a three-dimensional version of the Seiberg-Witten equations.
- OSTI ID:
- 22162715
- Journal Information:
- Journal of Mathematical Physics, Vol. 54, Issue 1; Other Information: (c) 2013 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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CORRELATIONS
DIFFERENTIAL EQUATIONS
DISLOCATIONS
GAUGE INVARIANCE
GINZBURG-LANDAU THEORY
KINETIC ENERGY
ORDER PARAMETERS
QUANTUM FIELD THEORY
REVIEWS
SPIN
SU-2 GROUPS
SUPERCONDUCTIVITY
SUPERCONDUCTORS
THREE-DIMENSIONAL CALCULATIONS
TORSION
UNITARY SYMMETRY