Phys. Rev. D 61, 104001 (2000) [13 pages]Fock representations from U(1) holonomy algebrasReceived 29 November 1999; published 4 April 2000 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 Poincaré 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. © 2000 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevD.61.104001
DOI:
10.1103/PhysRevD.61.104001
PACS:
04.60.Ds, 03.65.Fd
|
|
About | Terms and Conditions | Subscriptions | Search | Help
Use of the American Physical Society websites and journals implies that the user has read and agrees to our Terms and Conditions and any applicable Subscription Agreement. Physical Review®, Physical Review Letters®, Reviews of Modern Physics®, and Physical Review Special Topics® are trademarks of the American Physical Society.