Classical Weyl-Spinor approach to U(1) and non-abelian local gauge theories

Abstract

In a previous paper we introduced two linear spinor equations equivalent to the Lorentz Force and stated that these equations were fairly general and could be applied to any force field compatible with Special Relativity. In this paper, via a lagrangian approach, we explore this possibility and obtain classical spinor equations describing the behaviour of fermionic particles not only under an electromagnetic field but also under Yang-Mills and Color fields. We find a covariant derivative defined {\it along the classical trajectory} of the particle, which can be extended to SU(2) and SU(3) local symmetries, and obtain the Yang-Mills and Color fields in a new classical Weyl-spinor approach to Gauge Theories. In the SU(3) case, the obtained equations which describe the behaviour of quarks under gluon fields could be in principle applied to the quark-gluon plasma phase existing during the first instants of the Universe.