Very special relativity and Lorentz violating theories

Very special relativity (VSR) keeps the main features of special relativity but breaks rotational invariance. We will show how VSR like terms which depend on a fixed null vector can be generated systematically. We start with a formulation for a spinning particle which incorporates VSR. We then use this formulation to derive the VSR modifications to the Maxwell equations. Next we consider VSR corrections to Thomas precession. We start with the coupling of the spinning particle to the electromagnetic field adding a gyromagnetic factor which gives rise to a magnetic moment. We then propose a spin vector in terms of the spinning particle variables and show that it obeys the BMT equation. All this is generalized to the VSR context and we find the VSR contributions to the BMT equation.