New diffeomorphism invariant states on a holonomy-flux algebra

TL;DR

This paper introduces a new class of diffeomorphism invariant states on a holonomy-flux algebra, challenging previous uniqueness results by relaxing certain assumptions in background independent quantum theories.

Contribution

It presents alternative assumptions under which non-unique diffeomorphism invariant states can exist on the algebra of quantum observables.

Findings

Existence of new invariant states under relaxed assumptions

Counterexamples to previous uniqueness theorems

Broader class of states in background independent quantum theories

Abstract

The theorem by Lewandowski et al. stating uniqueness of a diffeomorphism invariant state on an algebra of quantum observables for background independent theories of connections is based on some technical assumptions imposed on the algebra and the diffeomorphisms. In this paper we present a class of diffeomorphism invariant states on an algebra of this sort, which exist when the algebra and the diffeomorphisms satisfy alternative assumptions.