Classical local SU(3) gauge invariance in Weyl 2-spinor language and quark–gluon plasma equations of motion

Abstract

In a new classical Weyl 2-spinor approach to non abelian gauge theories, starting with the U(1) gauge group in a previous work, we study now the SU(3) case corresponding to quarks (antiquarks) interacting with color fields. The principal difference with the conventional approach is that particle-field interactions are not described by means of potentials but by the field strength magnitudes. Some analytical expressions showing similarities with electrodynamics are obtained. Classical equations that describe the behavior of quarks under gluon fields might be in principle applied to the quark–gluon plasma phase existing during the first instants of the Universe.