Bessel-X waves: superluminal propagation and the Minkowski space-time
  Superluminal behavior has been extensively studied in recent years, especially with regard to the topic of superluminality in the propagation of a signal. Particular interest has been devoted to Bessel-X waves propagation, since some experimental results showed that these waves have both phase and group velocities greater that light velocity c. However, because of the lack of an exact definition of signal velocity, no definite answer about the signal propagation (or velocity of information) has been found. The present paper is a short note that deals in a general way with this vexed question. By analyzing the field of existence of the Bessel X-wave in pseudo-Euclidean space-time, it is possible to give a general description of the propagation, and to overcome the specific question related to a definition of signal velocity. 
D. Mugnai