2000/01/19 by Madhavan Varadarajan · 1 citation
Mathematics · Physics and Astronomy · #Abelian group #Advanced Topics in Algebra #Algebra over a field #Algorithm #Black Holes and Theoretical Physics #Fock space #Holonomy #Loop quantum gravity #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantization (signal processing) #Quantum #Quantum gravity #Quantum mechanics #gr-qc
paper · pdf · doi:10.1103/physrevd.61.104001
published as Phys.Rev. D61 (2000) 104001 · Latex file, 30 pages, to appear in Phys Rev D
arxiv created 2000/01/19 · openalex publication_date 2000/04/04 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We examine the quantization of U(1) holonomy algebras using the Abelian C* algebra based techniques which form the mathematical underpinnings of current efforts to construct loop quantum gravity. In particular, we clarify the role of ``smeared loops'' and of Poincar'e invariance in the construction of Fock representations of these algebras. This enables us to critically reexamine early pioneering efforts to construct Fock space representations of linearized gravity and free Maxwell theory from holonomy algebras through an application of the (then current) techniques of loop quantum gravity.