Towards new background independent representations for loop quantum gravity

2007/09/11 by Madhavan Varadarajan
Mathematics · Medicine · Physics and Astronomy · #Black Holes and Theoretical Physics #Gauge (firearms) #Gauge group #Gauge theory #Independence (probability theory) #Loop (graph theory) #Loop quantum gravity #Mathematical analysis #Mathematical physics #Mathematics #Neuroblastoma Research and Treatments #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum #Quantum gravity #Quantum mechanics #Representation (politics) #Simplicity #Spin foam #Theoretical physics #Uniqueness #gr-qc

paper · pdf · doi:10.1088/0264-9381/25/10/105011

published as Class.Quant.Grav.25:105011,2008 · 22 pages, minor changes

arxiv created 2007/09/11 · openalex publication_date 2008/05/01 · arxiv updated 2015/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 Lewandowski–Okolow–Sahlmann–Thiemann (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).

Citations

• Background independent quantizations—the scalar field: II
• Irreducibility of the Weyl Algebra in Loop Quantum Gravity
• Uniqueness of Diffeomorphism Invariant States on Holonomy–Flux Algebras
• Projective techniques and functional integration for gauge theories
• Automorphism covariant representations of the holonomy-flux lowast-algebra