Compact phase space, cosmological constant, discrete time

Abstract

We study the quantization of geometry in the presence of a cosmological constant, using a discretiza- tion with constant-curvature simplices. Phase space turns out to be compact and the Hilbert space finite dimensional for each link. Not only the intrinsic, but also the extrinsic geometry turns out to be discrete, pointing to discreetness of time, in addition to space. We work in 2+1 dimensions, but these results may be relevant also for the physical 3+1 case.

6 pages

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Cited by in corpus (18)

• Quantum gravity kinematics from extended TQFTs
• On the possibility of experimental detection of the discreteness of time
• Towards the map of quantum gravity
• Bounds on quantum gravity parameter from the $SU(2)$ NJL effective model of QCD
• Ashtekar-Barbero holonomy on the hyperboloid: Immirzi parameter as a Cut-off for Quantum Gravity
• Late time cosmic acceleration from natural infrared cutoff?
• SU(2) Flat Connection on Riemann Surface and Twisted Geometry with Cosmological Constant
• Coupled intertwiner dynamics: A toy model for coupling matter to spin foam models
• Noncommutative spaces and covariant formulation of statistical mechanics
• A new realization of quantum geometry
• Quantum Hubble horizon
• Minisuperspace model of compact phase space gravity
• Entropy bound for the photon gas in noncommutative spacetime
• On the Hydrogen Atom in the Holographic Universe
• Modular polymer representations of the Weyl algebra
• UV dimensional reduction to two from group valued momenta
• Effective dimensions of infinite-dimensional Hilbert spaces: A phase-space approach
• Quantum variational solving of the Wheeler-DeWitt equation