Discretization of space-time is a necessary
step in quantizing gauge theories, including
gravity, when, as a result of quantization,
the gaugegroup becomes finite and infenetezimal
transformations sieze to make sense. We
identify a minimal set of variables of
discretized gravity on which Newtonian
interaction between two particles can be
calculated. The space is discretized by
dividing it into quadrants by three
three-dimensional surfaces intersecting at the
worldlines of the particles. The variables
needed for calculating Newtonian potential are
the holonomies of $SO(4,1)$ connection dual to
the above three surfaces plus the holonomies
around the images of the particle worldlines on
every surface. The equations of motions for
these variables are ordinary differential
equations with no spatial derivatives.
Newtonian portential in the usual form is
reproduced from linearized version of these
equations, in which the holonomies of $SO(4,1)$
group are replaced by abelian holonomies of
$so(4,1)$ algebra. The full equations with
$SO(4,1)$ holonomies indicate the presence of
a lower bound on the distance between the
particles. In the limit when one particle has
much bigger mass than the other, this bound
corresponds to the Schwarzschild radius of the
heavy particle. We discuss the possible
implications of this effect for short dictance
physics in quantum theory.