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 u}rightarrow Box^n G_{mu u} $ in the action. The $n=0$ case restores back to the standard abelian gauge field theory. The equation of motion and Noethers conserved current of the theory are also studied.
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