Hamiltonian analysis for Lifshitz type Fields

Abstract

Using the Dirac Method, we study the Hamiltonian consistency for three field theories. First we study the electrodynamics a la Ho\v{r}ava and we show that this system is consistent for an arbitrary dynamical exponent $z.$ Second, we study a Lifshitz type electrodynamics, which was proposed in [1]. For this last system we found that the canonical momentum and the electrical field are related through a Proca type Green function, however this system is consistent. In addition, we show that the anisotropic Yang-Mills theory with dynamical exponent $z=2$ is consistent. Finally, we study a generalized anisotropic Yang-Mills theory and we show that this last system is consistent too.