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arXiv · gr-qc/0302059

Diffeomorphism covariant representations of the holonomy-flux star-algebra

Andrzej Okolow·Jerzy Lewandowski
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Abstract

Recently, Sahlmann proposed a new, algebraic point of view on the loop quantization. He brought up the issue of a star-algebra underlying that framework, studied the algebra consisting of the fluxes and holonomies and characterized its representations. We define the diffeomorphism covariance of a representation of the Sahlmann algebra and study the diffeomorphism covariant representations. We prove they are all given by Sahlmann's decomposition into the cyclic representations of the sub-algebra of the holonomies by using a single state only. The state corresponds to the natural measure defined on the space of the generalized connections. This result is a generalization of Sahlmann's result concerning the U(1) case.

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Andrzej Okolow, Jerzy Lewandowski. 2003-06-24. Diffeomorphism covariant representations of the holonomy-flux star-algebra. https://doi.org/10.1088/0264-9381%2F20%2F16%2F302

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