Electrodynamics a la Horava

TL;DR

This paper explores an anisotropic electrodynamics framework with arbitrary dynamic exponent z, deriving equations, conserved quantities, and analyzing modifications to fundamental constants and duality properties.

Contribution

It introduces a consistent electrodynamics with anisotropic space-time transformations and examines its physical implications and duality structure.

Findings

Propagator as a quantum correction to the usual propagator

Conservation laws for momentum and angular momentum are modified

Speed of light and electric charge depend on the dynamic exponent z

Abstract

We study an electrodynamics consistent with anisotropic transformations of space-time with an arbitrary dynamic exponent $z$. The equations of motion and conserved quantities are explicitly obtained. We show that the propagator of this theory can be regarded as a quantum correction to the usual propagator. Moreover we obtain that both the momentum and angular momentum are not modified, but their conservation laws do change. We also show that in this theory the speed of light and the electric charge are modified with $z$. The magnetic monopole in this electrodynamics and its duality transformations are also investigated. For that we found that there exists a dual electrodynamics, with higher derivatives in the electric field, invariant under the same anisotropic transformations.