Speaker
Description
Smolin's weak Newton constant limit of 4D Euclidian signature vacuum general relativity, mathematically a consisten U(1)$^3$ deformation of SU(2) quantum gravity, has recently been shown to be quantum integrable, that is, the canonical quantisation programme can be completed. An explicit quantum representation of the Bergmann Komar "group" (the "exponentiation" of the hypersurface deformation "algebra") can be found and the physical Hilbert space, the physical Hamiltonian and the quantum algebra of Dirac observables can be constructed. A cosmological constant can be included and an extension to Lorentzian signature is possible. The model thus appears to be an ideal testing ground for all approaches to quantum gravity -- a "quantum gravity harmonic oscillator". In this talk, these developments, which crucially rest on the non-degeneracy of quantum metrics, will be summarised and possible consequences for actual quantum gravity will be discussed.
