Compact phase space, cosmological constant, discrete time

Carlo Rovelli (1, 2) , Francesca Vidotto (3)

1 CPT - Centre de Physique Théorique - UMR 7332
2 CPT - E4 Gravité quantique
3 IMAPP - Institute for Mathematics, Astrophysics and Particle Physics

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.

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]; Physique mathématique [math-ph]

Carlo Rovelli, Francesca Vidotto. Compact phase space, cosmological constant, discrete time. Physical Review D, 2016, 91 (8). ⟨hal-01476562⟩