The complete spectrum of the area from recoupling theory in loop quantum gravity

TL;DR

This paper calculates the full spectrum of the area operator in loop quantum gravity using recoupling theory, including the degenerate sector, and confirms consistency with previous connection-representation results.

Contribution

It provides the complete area spectrum in loop quantum gravity, extending prior work by incorporating the degenerate sector and aligning with connection-representation findings.

Findings

Complete spectrum of the area operator derived

Inclusion of the degenerate sector confirmed

Results agree with connection-representation spectrum

Abstract

We compute the complete spectrum of the area operator in the loop representation of quantum gravity, using recoupling theory. This result extends previous derivations, which did not include the ``degenerate'' sector, and agrees with the recently computed spectrum of the connection-representation area operator.