ELECTRODYNAMICS à la HOŘAVA

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.

Lifshitz field theories, Snyder noncommutative spacetime and momentum-dependent metric

“…which is the action for the anisotropic electrodynamics field with dynamic exponent z = 2, [48]. Then, this last system can be seen as an electrodynamics in a metric depending on the momenta.…”

“…Hořava gravity has different interesting properties, some of them are [37,38,39,40,41,42,43,44,45]. Field theories invariant under the anisotropic scaling transformations (2) can be seen in [46,47,48,49,50,51,52,53,54,55,56], notably these field theories improve their high energy behavior. Furthermore, in the usual general relativity it has been found space-times invariant under the anisotropic scaling (2), see [57].…”

Hamiltonian analysis for Lifshitz type fields

“…In this section we study the Hamiltonian formalism for the anisotropic electrodynamics, the action for this system is given by [12]…”

“…Amazingly, the gravity/gauge correspondence allows a relation between different metrics invariant under the anisotropic scaling (1) and some condensed matter systems [7,8,9]. Furthermore, almost every field theory can be transformed into a field theory invariant under the anisotropic scaling (1), this deformed field theory improves its high energy behavior [10,11,12,13,14,15,16]. In fact, using the anisotropic scalings (1), Hořava formulated a modified gravity which seems to be free ghosts and power counting renormalizable for z = 3 [17].…”

Matter in Hořava-Lifshitz gravity

“…We also consider a vector field A µ invariant under a U (1) gauge symmetry (see also [24]). Our analysis will run along much the same lines as for the scalar field.…”