We assume that the points in volumes smaller than an elementary volume (which may have a Planck size) are indistinguishable in any physical experiment. This naturally leads to a picture of a discrete space with a finite number of degrees of freedom per elementary volume. In such discrete spaces, each elementary cell is completely characterized by displacement operators connecting a cell to the neighboring cells and by the spin connection. We define the torsion and curvature of the discrete spaces and show that in the limiting case of vanishing elementary volume the standard results for the continuous curved differentiable manifolds are completely reproduced.
By Alessandra Buonanno
By David Shoemaker
By Sebastiano Bernuzzi
By Marc Henneaux
By Sergey Solodukhin
By Piotr Jaranowski
By Bala Iyer
By Giuseppe Policastro
By Remo Ruffini
By Michael Kramer
By Manuel Rodrigues
By Leor Barack
By Misha Gromov
By Misha Gromov
By Eleni-Alexandra Kontou
