Symmetry and Evolution in Quantum Gravity

Sean Gryb*, Karim Thebault

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

13 Citations (Scopus)


We propose an operator constraint equation for the wavefunction of the Universe that admits genuine evolution. While the corresponding classical theory is equivalent to the canonical decomposition of General Relativity, the quantum theory contains an evolution equation distinct from standard Wheeler-DeWitt cosmology. Furthermore, the local symmetry principle-and corresponding observables-of the theory have a direct interpretation in terms of a conventional gauge theory, where the gauge symmetry group is that of spatial conformal diffeomorphisms (that preserve the spatial volume of the Universe). The global evolution is in terms of an arbitrary parameter that serves only as an unobservable label for successive states of the Universe. Our proposal follows unambiguously from a suggestion of York whereby the independently specifiable initial data in the action principle of General Relativity is given by a conformal geometry and the spatial average of the York time on the spacelike hypersurfaces that bound the variation. Remarkably, such a variational principle uniquely selects the form of the constraints of the theory so that we can establish a precise notion of both symmetry and evolution in quantum gravity.

Original languageEnglish
Pages (from-to)305-348
Number of pages44
JournalFoundations of Physics
Issue number3
Publication statusPublished - Mar 2014


  • Canonical quantization
  • Gauge symmetry
  • Problem of time
  • quantum cosmology
  • Quantum gravity
  • Variational principles


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