In the usual quantum theory of fields, as described in the Minkowski space-time, the concepts of particle and antiparticle appear associated with positive and negative energy states respectively. In this article, which is directed to graduate students in physics, we discussed in a pedagogical way how these concepts can be transferred when we make a change of coordinates, from the Minkowski space-time to the coordinates of the light cone. We conclude that these new coordinates have an arbitrary choice, once the sign of the energy is coupled to the sign of the longitudinal component of the momentum in the light cone. Although there is this arbitrariness, the sign correlation between the energy and the longitudinal momentum implies profound physical consequences. Positive momenta imply positive energy, and negative momenta imply negative energies. This means, for example, that in the quantum vacuum of the light front there cannot be any pair production of particle and antiparticle, unlike what happens in the usual Minkowski space.
Keywords:
quantum theory of fields; Minkowski space; light cone; antiparticles