Covariance in models of loop quantum gravity: Spherical symmetry

Abstract

Spherically symmetric models of loop quantum gravity have been studied recently by different methods that aim to deal with structure functions in the usual constraint algebra of gravitational systems. As noticed by Gambini and Pullin, a linear redefinition of the constraints (with phase-space dependent coefficients) can be used to eliminate structure functions, even Abelianizing the more-difficult part of the constraint algebra. The Abelianized constraints can then easily be quantized or modified by putative quantum effects. As pointed out here, however, the method does not automatically provide a covariant quantization, defined as an anomaly-free quantum theory with a classical limit in which the usual (off-shell) gauge structure of hypersurface deformations in space-time appears. The holonomy-modified vacuum theory based on Abelianization is covariant in this sense, but matter theories with local degrees of freedom are not. Detailed demonstrations of these statements show complete agreement with results of canonical effective methods applied earlier to the same systems (including signature change).

29 pages

References in corpus (10)

• Anomaly freedom in perturbative loop quantum gravity
• Spherically Symmetric Quantum Geometry: States and Basic Operators
• Quantum field theory on a cosmological, quantum space-time
• Non-marginal LTB-like models with inverse triad corrections from loop quantum gravity
• Effective Constraints for Quantum Systems
• Uniform discretizations: a new approach for the quantization of totally constrained systems
• Covariance in models of loop quantum gravity: Gowdy systems
• Spherically symmetric canonical quantum gravity
• Information loss, made worse by quantum gravity?
• Quantum space-time of a charged black hole

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