Proca equation and vector field quantization in a rotating system

A strong background field drastically changes the vacuum structure and proper basis of a system in both classical and quantum mechanics,e.g.,the Landau levels in a background magnetic field.This is true even for a rotating system.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 study,we completed the first step for the spin-1 field,which includes solving the Proca equation in the presence of a background rotation and completing its canonical quantization.We show that because of the symmetry,the eigen states are actually the same as those of Maxwell equations in cylindrical coordinates.The propagator as well as the near-central approximation were obtained by assuming that the vorticity areas are very small in the relativistic QGP.