Abstract: We try to investigate a generalization of the Heisenberg commutation re- lation [p; q] = ô€€€i}, introduced by Chamseddine, Connes and Mukhanov as \the one-sided and the two-sided quantization equations", which captures the geometry. The momentum variable p is encoded by the Dirac operator and the analogue of the position variable q is the Feynman slash of real scalar elds over a closed even-dimensional spin manifold. Existence of a solution of the one-sided equation implies that the manifold decomposes into a dis- connected sum of spheres of unit volume which represent quanta of geometry. The two-sided equation, as the rened version of the one-sided equation by involving the real structure on a spin manifold, implies the quantization of the volume of the spin manifold.