  Motivated by both concepts of R.J. Adler's recent work on utilizing Clifford
algebra as the linear line element $ds = \left\langle \gamma_\mu \right\rangle
dX^\mu $, and the fermionization of the cylindrical worldsheet Polyakov action,
we introduce a new type of spacetime quantization that is fully covariant. The
theory is based on the reinterpretation of Adler's linear line element as $ds =
\gamma_\mu \left\langle \lambda \gamma ^\mu \right\rangle$, where $\lambda$ is
the characteristic length of the theory. We name this new operator as
"spacetime interval operator", and argue that it can be regarded as a natural
extension to the one-forms in the $U(\mathfrak{s}u(2))$ non-commutative
geometry. By treating Fourier momentum as the particle momentum, the
generalized uncertainty principle of the $U(\mathfrak{s}u(2))$ non-commutative
geometry, as an approximation to the generalized uncertainty principle of our
theory, is derived, and is shown to have a lowest order correction term of the
order $p^2$ similar to that of Snyder's. The holography nature of the theory is
demonstrated, and the predicted fuzziness of the geodesic is shown to be much
smaller than conceivable astrophysical bounds.
