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arxiv: hep-th/0501114 · v4 · submitted 2005-01-14 · ✦ hep-th · gr-qc

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Loop quantum gravity: an outside view

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classification ✦ hep-th gr-qc
keywords gravityquantumconstraintloopachievementsalgebraambiguitiesappearance
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We review aspects of loop quantum gravity in a pedagogical manner, with the aim of enabling a precise but critical assessment of its achievements so far. We emphasise that the off-shell (`strong') closure of the constraint algebra is a crucial test of quantum space-time covariance, and thereby of the consistency, of the theory. Special attention is paid to the appearance of a large number of ambiguities, in particular in the formulation of the Hamiltonian constraint. Developing suitable approximation methods to establish a connection with classical gravity on the one hand, and with the physics of elementary particles on the other, remains a major challenge.

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