Discrete Symmetries in Covariant LQG

Understand

We study time-reversal and parity ---on the physical manifold and in internal space--- in covariant loop gravity.

• We consider a minor modification of the Holst action which makes it transform coherently under such transformations.
• The classical theory is not affected but the quantum theory is slightly different.
• In particular, the simplicity constraints are slightly modified and this restricts orientation flips in a spinfoam to occur only across degenerate regions, thus reducing the sources of potential divergences.