Abstract
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 spin particle and the corresponding antiparticle.
Notes
1 The Dirac matrices are defined as: i = 1, 2, 3, where
are the Pauli matrices, and