  A pseudoclassical model, reproducing, upon quantization, the dynamics of the
chiral sectors of the massless spin-1/2 field theory is proposed. The discrete
symmetries of the action are studied in details. In order to reproduce the
positive and negative chiral sectors of the particle and antiparticle, we
promote the algebra of functions on the phase space to a bimodule over the
complexified quaternions - biquaternions. The quantization is performed by
means of strictly canonical methods (Dirac brackets formalism) reproducing the
Dirac equation in the Foldy-Wouthuysen representation in the particle and
antiparticle sectors and the Weyl equation in the chiral sectors.

High Energy Physics - Theory