Area bounds and gauge fixing: alternative canonical variables for loop gravity

TL;DR

This paper introduces a canonical parametrization of twisted geometries in loop quantum gravity, providing analytical bounds on area evolution and simplifying gauge fixing, with implications for understanding bounce phenomena.

Contribution

It establishes an explicit correspondence between twisted geometries and frame/spinorial descriptions, and generalizes gauge fixing methods beyond two-vertex models.

Findings

Analytical bounds on total area evolution show a non-zero lower bound at finite times.

The framework suggests a bounce-like behavior in the quantum geometry.

Canonical variables simplify gauge fixing procedures for complex configurations.

Abstract

We use a canonical parametrization of twisted geometries describing the classical phase space of loop quantum gravity on a fixed graph, and establish its explicit correspondence with the associated frame bases and spinorial descriptions. Applied to the two-vertex model, this framework yields analytical bounds on the evolution of the total area, proving the existence of a non-vanishing lower bound at finite times. These findings, previously observed only numerically, suggest a bounce-like behavior and highlight the usefulness of these variables for the study of more general configurations. As a second result, the canonical variables are shown to simplify the gauge-fixing procedure, generalizing previous results restricted to two-vertex models with four links.