Loop quantum gravity and cosmology

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Abstract

“It would be permissible to look upon the Hamiltonian form as the fundamental one, and there would then be no fundamental four-dimensional symmetry in the theory. One would have a Hamiltonian built up from four weekly [sic] vanishing functions, given by [the Hamiltonian and diffeomorphism constraints]. The usual requirement of four-dimensional symmetry in physical laws would then get replaced by the requirement that the functions have weakly vanishing P.B.'s, so that they can be provided with arbitrary coefficients in the equations of motion, corresponding to an arbitrary motion of the surface on which the state is defined.” P. A. M. Dirac, in “The theory of gravitation in Hamiltonian form,” Proc. Roy. Soc. A 246 (1958) 333-43. Introduction In its different incarnations, quantum gravity must face a diverse set of fascinating problems and difficulties, a set of issues best seen as both challenges and opportunities. One of the main problems in canonical approaches, for instance, is the issue of anomalies in the gauge algebra underlying space-time covariance. Classically, the gauge generators, given by constraints, have weakly vanishing Poisson brackets with each other: they vanish when the constraints are satisfied. After quantization, the same behavior must be realized for commutators of quantum constraints (or for Poisson brackets of effective constraints), or else the theory becomes inconsistent due to gauge anomalies. If and how canonical quantum gravity can be obtained in an anomaly-free way is an important question, not yet convincingly addressed in full generality.

Original languageEnglish (US)
Title of host publicationFoundations of Space and Time
Subtitle of host publicationReflections on Quantum Gravity
PublisherCambridge University Press
Pages211-256
Number of pages46
Volume9780521114400
ISBN (Electronic)9780511920998
ISBN (Print)9780521114400
DOIs
StatePublished - Jan 1 2012

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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    Bojowald, M. (2012). Loop quantum gravity and cosmology. In Foundations of Space and Time: Reflections on Quantum Gravity (Vol. 9780521114400, pp. 211-256). Cambridge University Press. https://doi.org/10.1017/CBO9780511920998.011