Towards new background independent representations for Loop Quantum Gravity

TL;DR

This paper investigates alternative background independent representations in Loop Quantum Gravity by relaxing the assumptions of the LOST theorem, focusing on the U(1) gauge group to explore new possibilities beyond the unique representation.

Contribution

It introduces weakened assumptions for background independence in Loop Quantum Gravity, expanding the space of possible representations beyond the established uniqueness theorem.

Findings

Existence of alternative representations under relaxed assumptions

Retention of background independence in new representations

Potential implications for the formulation of Loop Quantum Gravity

Abstract

Recently, uniqueness theorems were constructed for the representation used in Loop Quantum Gravity. We explore the existence of alternate representations by weakening the assumptions of the so called LOST uniqueness theorem. The weakened assumptions seem physically reasonable and retain the key requirement of explicit background independence. For simplicity, we restrict attention to the case of gauge group U(1).