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Résumé |
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. Motivated by the definition of Dirac operator in lattice gauge
theories, and the gauge formulation of gravity, 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. |
