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 Hoˇrava 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.