Area spectrum in Lorentz covariant loop gravity

TL;DR

This paper computes the eigenvalues of the area operator in Lorentz covariant loop gravity, revealing a spectrum expressed via quadratic Casimir operators without dependence on the Immirzi parameter.

Contribution

It introduces a modified loop state definition suitable for non-commutative connections and diagonalizes the area operator within a Lorentz covariant framework.

Findings

Eigenvalues expressed through quadratic Casimir operators

No dependence on the Immirzi parameter

Modified loop states for non-commutative connections

Abstract

We use the manifestly Lorentz covariant canonical formalism to evaluate eigenvalues of the area operator acting on Wilson lines. To this end we modify the standard definition of the loop states to make it applicable to the present case of non-commutative connections. The area operator is diagonalized by using the usual shift ambiguity in definition of the connection. The eigenvalues are then expressed through quadratic Casimir operators. No dependence on the Immirzi parameter appears.