Discrete Symmetries in Covariant LQG

TL;DR

This paper investigates how discrete symmetries like time-reversal and parity affect covariant loop quantum gravity, proposing a modification to the Holst action that influences quantum properties and divergence sources.

Contribution

It introduces a minor modification to the Holst action that preserves classical physics but alters quantum simplicity constraints, reducing divergence sources in spinfoam models.

Findings

Quantum theory differs slightly due to modified simplicity constraints.

Orientation flips in spinfoam are restricted to degenerate regions.

Potential divergences in the quantum theory are reduced.

Abstract

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.