On the Quantization of Length in Noncommutative Spaces

We consider canonical/Weyl-Moyal type noncommutative (NC) spaces with rectilinear coordinates. Motivated by the analogy of formalism quantum mechanical harmonic oscillator problem in phase-space that canonical-type NC 2-D space, and noting square length latter case is analogous to Hamiltonian former case, we arrive at conclusion area are quantized such an if expressed entirely terms length. extend our analysis 3-D formulate a ladder operator approach quantization space. However, method does not lend itself spacetime 1 + id="M2"> 2 Minkowski spacetimes noncommutativity between time space considered. If taken commute spatial coordinates maintained only among id="M3"> id="M4"> 3 dimensional spacetime, then possible approach.