  A strong background field will change the vacuum structure and the proper
basis of a system drastically in both classical and quantum mechanics, e.g. the
Landau levels in a background magnetic field. The situation is the same for the
rotating case. In such a system the usual set of plane-wave states would no
longer be suitable as a starting point of perturbation. Alternatively and
straightforwardly in a rapidly and globally rotating system, it is better to
reformulate the perturbation computation in principle. In this work we will
complete the first step for the spin-1 field, which includes solving the Proca
equation in present of a background rotation and complete its canonical
quantization. It will be shown that because of the symmetry the eigen states
are actually the same as the ones of Maxwell equations in cylindrical
coordinate. The propagator as well as the near-central approximation will be
obtained by considering the vorticity areas are so small in the relativistic
QGP.
