Geodesic
New approach to calculating the spectrum of a quantum space–time
Teoretičeskaâ i matematičeskaâ fizika, Tome 190 (2017) no. 3, pp. 511-518 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the dynamics of a massive pointlike particle coupled to gravity in four space–time dimensions. It has the same degrees of freedom as an ordinary particle{:} its coordinates with respect to a chosen origin (observer) and the canonically conjugate momenta. The effect of gravity is that such a particle is a black hole: its momentum becomes spacelike at a distances to the origin less than the Schwarzschild radius. This happens because the phase space of the particle has a nontrivial structure: the momentum space has curvature, and this curvature depends on the position in the coordinate space. The momentum space curvature in turn leads to the coordinate operator in quantum theory having a nontrivial spectrum. This spectrum is independent of the particle mass and determines the accessible points of space–time.
Keywords: quantization of gravity, conformal field theory, space–time discreteness
Mots-clés : Planck scale. 
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A. N. Starodubtsev. New approach to calculating the spectrum of a quantum space–time. Teoretičeskaâ i matematičeskaâ fizika, Tome 190 (2017) no. 3, pp. 511-518. http://geodesic.mathdoc.fr/item/TMF_2017_190_3_a11/

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