Anomaly-free representations of the holonomy-flux algebra

TL;DR

This paper investigates the uniqueness of representations of the holonomy-flux algebra in loop quantum gravity, showing that for analytic diffeomorphisms, flux operators are restricted to constant functions in anomaly-free representations, aligning with the standard model.

Contribution

It demonstrates that in anomaly-free representations, flux operators must be constant functions, reinforcing the uniqueness of the standard representation in loop quantum gravity.

Findings

Flux operators are only constants in anomaly-free representations for analytic diffeomorphisms.

Standard representation flux operators are zero.

Supports the uniqueness of the standard representation in loop quantum gravity.

Abstract

We work on the uniqueness, gr-qc/0504147, of representations of the holonomy-flux algebra in loop quantum gravity. We argue that for analytic diffeomorphisms, the flux operators can be only constants as functions on the configuration space in representations with no anomaly, which are zero in the standard representation.