The two-component spinor field

Abstract

We present a theory of the classical two-component spinor field, and its interpretation as a wave function in relativistic quantum mechanics. Contrary to the classical Dirac bispinor field, this spinor field gives rise to a conserved indefinite charge, which is the basis of the probabilistic interpretation of the wave function. We first present the theory of a spin- 1 2 particle in an external electromagnetic field, which is then extended to several identical fermions. We are dealing with a theory of a fixed number of particles, in which pair annihilation and creation appear in the form of a reflection of the wave packet by a potential barrier on the time axis, which changes the mode of propagation of a particle from forward to backward in time and viceversa. We also present the theory of the interaction with a dynamical electromagnetic field, in a gauge-independent, Lorentz-covariant, observer-dependent formulation. A brief discussion of the possible quantization procedures, using commutators or anticommutators, for the spinor field follows.