Spin connection of twisted geometry

H. M. Haggard, C. Rovelli, F. Vidotto and W. Wieland

Physical Review D 87 (024038), 2013.

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.

DOI: 10.1103/PhysRevD.87.024038

Full text: HaRoViWiTwistedSpinConnection.pdf