  Gauge field theory is a quantum field theory that describes the interaction
of elementary spin-1 particles, of which being massless to preserve gauge
symmetry. In this paper, we give a generalized, extended study for abelian
gauge field theory under successive rotor model in general $D$-dimensional
spacetime, and establish a theorem that $n$ rotor contributes to the $\Box^n
T^{\mu}$ fields in the integration-by-part formalism of the action. The $n=0$
case corresponds to the standard abelian gauge field theory.
