  Recently, a number of experimental observations on the superluminal group
velocities of pulses propagating in dispersive media have led to reconsidering
electromagnetism theory in an unconventional framework. To consider
faster-than-light phenomena, it is not necessary to replace the current
relativistic theory, but it is sufficient to extend it to superluminal motions
in a way that preserves the principle of causality. In the present paper, a new
approach to study superluminal motions is proposed, which avoids introducing
unphysical complex quantities and allows for the formulation of equations that
are covariant according to a hyperbolic metric. In the framework of this
formalism, Maxwell equations and the single-photon wave equation are obtained
through superluminal transformations of ordinary equations. It is shown that
the covariant and contravariant components of the superluminal electromagnetic
field determine its magnitude and direction, respectively. Furthermore, the
solutions of the transformed Maxwell equations are X-shaped ways propagating in
the superluminal spacetime region that is delimited by the infinite light cone
and the two-sheet hyperboloid perpendicular to it. Instead, in quantum
mechanics, the covariant and contravariant components of the electromagnetic
field are proportional to the right- and left-handed helicities of the single
photon, respectively.
