  In the preceding paper [arXiv:hep-th/0604217], we construct the Dirac
operator and the integral on the canonical noncommutative space. As a matter of
fact, they are ones on the noncommutative torus. In the present article, we
introduce the method to extend to the Minkowskian and Euclidean cases. As a
concluding remark, we present a geometrical notion of our gauge theory.
