• DOI:10.1007/s10701-014-9789-x
• Corpus ID: 118432028

Symmetry and Evolution in Quantum Gravity

@article{Gryb2014SymmetryAE,
  title={Symmetry and Evolution in Quantum Gravity},
  author={Sean B. Gryb and Karim Th{\'e}baault},
  journal={Foundations of Physics},
  year={2014},
  volume={44},
  pages={305-348}
}

• S. Gryb, Karim Thébaault
• Published 28 March 2013
• Physics, Mathematics
• Foundations of Physics

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.