Hamiltonian analysis for Lifshitz type Fields

TL;DR

This paper applies the Dirac method to analyze the Hamiltonian consistency of various Lifshitz-type field theories, including electrodynamics and Yang-Mills theories, demonstrating their consistency across different dynamical exponents.

Contribution

It provides a Hamiltonian consistency analysis for Lifshitz-type electrodynamics and Yang-Mills theories, establishing their viability for arbitrary and specific dynamical exponents.

Findings

Electrodynamics a la Horava is consistent for any dynamical exponent z.

Lifshitz electrodynamics is consistent with a Proca-like relation between momentum and electric field.

Anisotropic Yang-Mills theory with z=2 is consistent.

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.