Official URL: <a href="http://dx.doi.org/10.1103/PhysRevB.86.035413AbstractWe">http://dx.doi.org/10.1103/PhysRevB.86.035413AbstractWe</a> present a model for the theoretical description of the dynamics of a system of spinor cavity polaritons in real space and time, accounting for all relevant types of the interactions and effective magnetic fields.