Loop quantum gravity: an outside view

Abstract

Abstract: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.

Probing the cosmological singularity with a particle

“…However, this issue seems to be still open due to the assumptions made in the process of truncating the infinite number degrees of freedom of the LQG to the finite number used in the LQC [30,31]. This model has also problems in obtaining an unique semi-classical approximations [32], which are required to link the quantum phase with the nearby classical phase in the evolution of the Universe. For response to [32] we recommend [33].…”

“…This model has also problems in obtaining an unique semi-classical approximations [32], which are required to link the quantum phase with the nearby classical phase in the evolution of the Universe. For response to [32] we recommend [33].…”

Loop and Spin Foam Quantum Gravity: A Brief Guide for Beginners

“…Instead, a survey of the possible terms arising in this computation has led to the conclusion that the commutator vanishes on a certain restricted 'habitat' of states [33,37,38], and that therefore the LQG constraint algebra closes without anomalies. By contrast, we have argued in [8] that this 'on shell closure' is not sufficient for a full proof of quantum spacetime covariance, but that a proper theory of quantum gravity requires a constraint algebra that closes 'off shell', i.e. without prior imposition of a subset of the constraints.…”

“…Finally, in any canonical approach there is the question whether one has succeeded in achieving (a quantum version of) full space-time covariance, rather than merely covariance under diffeomorphisms of the three-dimensional slices. In [8] we have argued (against a widely held view in the LQG community) that for this, it is not enough to check the closure of two Hamiltonian constraints on diffeomorphism invariant states, but that it is rather the offshell closure of the constraint algebra that should be made the crucial requirement in establishing quantum space-time covariance.…”

“…In writing the above equations, we have thus been (and will be) cavalier about habitat questions and the precise definition of the Hamiltonian; see, however [8,33,38] for further details and critical comments.…”