A Transport Theory Route to the Dirac Equation

Starting from the similarity between the spherical harmonics approximation of order one to the linear transport equation (usually referred as P1 approximation) and the Klein-Gordon equation of the quantum physics, an extended set of equations is introduced, which is proved to be equivalent to the Dirac equation with imaginary mass. Conversely, when a real mass is restored into the extended P1 system, a new equation is obtained, whose solutions are superposition of the spinors for a 12− spin particle and the corresponding antiparticle.