3+1 Formulation of electrodynamics in Horava-Lifshitz gravity

Full text: We review the decomposition of space-time used in the ADM formulation of General Relativity to write the action of a source-free electromagnetic field which behaves as a test fluid on curved space. With the Hamiltonian written in this way, it is possible to find the additional terms which arise from the weaker symmetry conditions imposed by the Horava-Lifshitz theory, which is based on foliation-preserving diffeomorphisms. We outline the desirable conditions of the new action: power-counting renormalizability and gauge invariance. The new action is expected to recover its usual form in the so-called IR limit, when Lorentz invariance is restored. The new terms should only be relevant in the UV limit of small scales, and their influence on the behavior of the electromagnetic field might provide new clues as to the general behavior of Horava-Lifshitz gravity. Our aim is to construct an action which exactly recovers the classical electromagnetic action at large scales. We do so by adding to it gauge-invariant kinetic terms which keep the action power-counting renormalizable under anisotropic scaling transformations. (author)