  Gauge field theory with rank-one field $T_{\mu}$ 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 of abelian gauge field theory under successive rotor model in
general $D$-dimensional flat spacetime for spin-1 particles in the context of
higher order derivatives. We establish a theorem that $n$ rotor contributes to
the $\Box^n T^{\mu}$ fields in the integration-by-parts formalism of the
action. This corresponds to the transformation of gauge field $T^{\mu}
\rightarrow \Box^n T^{\mu}$ and gauge field strength $G_{\mu\nu}\rightarrow
\Box^n G_{\mu\nu} $ in the action. The $n=0$ case restores back to the standard
abelian gauge field theory. The equation of motion and Noether's conserved
current of the theory are also studied.
