QUANTUM GRAVITY DYNAMICS AND QUANTUM SPACE-TIME

We study gravity in the context of the non-commutative manifold 42 MZ , where the discrete space 2 Z represents a direction-vector associated with a space-time point.The pertinent geometry involves the non-commutativity parameter provided by the field strength associated with (2, ) SL C gauge fields and is dependent on the phase space variables.The topological current associated with the gauge fields produces torsion when general relativity takes the form of teleparallel gravity.This inevitably leads to Weitzenbock geometry, which creates the deformed space-time.