Fetching the paper…

Reading the bibliography…

The spin connection of twisted geometry · Around

2012

The spin connection of twisted geometry

Haggard, Hal M., Rovelli, Carlo, Vidotto, Francesca et al.

Original
PDF
Post on X

Understand

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.

Built on

C. Rovelli and L. Smolin, “Discreteness of area and volume in quantum gravity,” Nucl. Phys
1995
Earlier work this paper cites.
A. Ashtekar, A. Corichi, and J. A. Zapata, “Quantum theory of geometry III: Noncommutativity of Riemannian structures,” Class.Quant.Grav
1998
Earlier work this paper cites.
Cambridge University Press, Cambridge, U.K., 2004
C. Rovelli, Quantum Gravity · 2004
Earlier work this paper cites.

Similar

A. Ashtekar and J. Lewandowski, “Background independent quantum gravity: A status report,” Class. Quant. Grav
2004
Cited alongside, same era.
Cambridge University Press, Cambridge, U.K., 2007
T. Thiemann, Modern Canonical Quantum General Relativity · 2007
Cited alongside, same era.
B. Dittrich and S. Speziale, “Area-angle variables for general relativity,” New J. Phys
Original
2008
Cited alongside, same era.
L. Freidel and S. Speziale, “From twistors to twisted geometries,” arXiv:1006.0199
Original
Cited in the paper.
M. Dupuis, J. P. Ryan, and S. Speziale, “Discrete gravity models and Loop Quantum Gravity: a short review,” arXiv:1204.5394
Original
Cited in the paper.
S. Speziale and W. M. Wieland, “The twistorial structure of loop-gravity transition amplitudes,” arXiv:1207.6348
Original
Cited in the paper.
C. Rovelli, “Zakopane lectures on loop gravity,” arXiv:1102.3660
Original
Cited in the paper.
E. Bianchi, “Loop Quantum Gravity à la Aharonov-Bohm,” arXiv:0907.4388
Original
Cited in the paper.
B. Dittrich and J. P. Ryan, “On the role of the Barbero-Immirzi parameter in discrete quantum gravity,” arXiv:1209.4892
Original
Cited in the paper.

Then

L. Freidel and S. Speziale, “Twisted geometries: A geometric parametrisation of SU(2) phase space,” Phys.Rev
Original
2010
Later among the works it cites.
C. Rovelli and S. Speziale, “On the geometry of loop quantum gravity on a graph,” Phys. Rev
Original
2010
Later among the works it cites.
B. Dittrich and J. P. Ryan, “Simplicity in simplicial phase space,” Phys. Rev
Original
2010
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…