Fock representations from U(1) holonomy algebras

Details Fock representations from U(1) holonomy algebras Fock representations from U(1) holonomy algebras

2000-01-19

arxiv.org/abs/gr-qc/0001050v1

Phys.Rev. D61 (2000) 104001

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Latex file, 30 pages, to appear in Phys Rev D

Scientific paper

10.1103/PhysRevD.61.104001

We revisit 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 Poincare invariance in the construction of Fock representations of these algebras. This enables us to critically re-examine early pioneering efforts to construct Fock space representations of linearised gravity and free Maxwell theory from holonomy algebras through an application of the (then current) techniques of loop quantum gravity.

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