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 Hořava and we show that this system is consistent for an arbitrary dynamical exponent z. Second, we study a Lifshitz type electrodynamics, which was proposed by Alexandre and Mavromatos [Phys. Rev. D 84, 105013 (2011)]. For this latter 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 system is consistent too.