Momentum and spin dynamics of photon in linear dielectric medium

The momentum of light in dielectric media has been a century-long controversy that continues to attract significant interest. In a linear dielectric medium with refractive index $n$, the momentum is predicted to be smaller by a factor of $n$ according to Max Abraham, and larger by the same factor according to Hermann Minkowski. By studying the coupled dynamics of photons and dipoles in a dielectric medium, we show that the change in momentum of the dipole corresponds to the Abraham momentum. On the other hand, the Minkowski momentum determines the direction of propagation and the precession of the photon spin, which is described by an SO(3) rotation.