Spin connection of twisted geometry

@article{Haggard2013SpinCO,
  title={Spin connection of twisted geometry},
  author={Hal M. Haggard and C. Rovelli and F. Vidotto and W. Wieland},
  journal={Physical Review D},
  year={2013},
  volume={87},
  pages={024038}
}
  • Hal M. Haggard, C. Rovelli, +1 author W. Wieland
  • Published 2013
  • Physics
  • Physical Review D
  • Twisted geometry is a piecewise-flat geometry less rigid than Regge geometry. In Loop Gravity, it provides the classical limit for each step of the truncation utilized in the definition of the quantum theory. We define the torsionless spin-connection of a twisted geometry. The difficulty given by the discontinuity of the triad is addressed by interpolating between triads. The curvature of the resulting spin connection reduces to the Regge curvature in the case of a Regge geometry. 

    Figures from this paper.

    Spinning geometry = Twisted geometry
    33
    Twisted geometries, twistors and conformal transformations
    12
    The closure constraint for the hyperbolic tetrahedron as a Bianchi identity
    13
    Edge modes of gravity -- III: Corner simplicity constraints
    3
    A note on the secondary simplicity constraints in loop quantum gravity
    21
    Quantum geometry from higher gauge theory
    3
    A discrete and coherent basis of intertwiners
    32

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 18 REFERENCES
    Twistors to twisted geometries
    102
    Quantum theory of geometry: III. Non-commutativity of Riemannian structures
    149
    Geometry of loop quantum gravity on a graph
    60
    Twistorial structure of loop-gravity transition amplitudes
    44
    Area?angle variables for general relativity
    120
    Loop Quantum Gravity à la Aharonov–Bohm
    21
    Simplicity in simplicial phase space
    57