For your equations to make sense, you have to specify a couple of things:

 - Specify how $\vec{k}$ is defined. For instance $$ \vec{k} =
    k^\mu\gamma_\mu $$
 - Specify how $k^\mu$ transform under Lorentz
   transformation.
 - Specify whether parameters $k^\mu$ are fundamental constants. And if they are not Lorentz scalar, how do you justify that fundamental constants are reference frame dependent?