Towards new background independent representations for 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).

22 pages, minor changes

References in corpus (3)

• Uniqueness of diffeomorphism invariant states on holonomy-flux algebras
• Background independent quantizations: the scalar field I
• Background independent quantizations: the scalar field II

Cited by in corpus (7)

• Quantum cosmology: a review
• Loop Quantum Gravity Vacuum with Nondegenerate Geometry
• From Classical To Quantum Gravity: Introduction to Loop Quantum Gravity
• On loop quantum gravity kinematics with non-degenerate spatial background
• The Koslowski- Sahlmann representation: Gauge and diffeomorphism invariance
• Structural aspects of loop quantum gravity and loop quantum cosmology from an algebraic perspective
• Towards Gaussian states for loop quantum gravity