The spin connection of twisted geometry

Abstract

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.

5 pages, 2 figures

References in corpus (5)

• From twistors to twisted geometries
• Area-angle variables for general relativity
• The twistorial structure of loop-gravity transition amplitudes
• Discrete Gravity Models and Loop Quantum Gravity: a Short Review
• On the role of the Barbero-Immirzi parameter in discrete quantum gravity

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