Flavour-mixing gauge field theory of massive Majorana neutrinos

Abstract

A gauge-field theory for massive neutral particles is developed on the basis of the real four-component Majorana equation. By use of its spin operator, a purely imaginary representation of the SU(2) algebra can be defined, which gives a covariant derivative that is real. Such a coupling to the gauge field preserves the real nature of the Majorana equation even when including interactions. As the associated isospin is four-dimensional, this procedure introduces four intrinsic degrees of freedom to the Majorana field, which may be related to four flavours. The main aim is to describe here the mathematical possibility for coupling Majorana particles with a gauge field which resembles that of the weak interaction. By adding a fourth member to the family, flavour could become a dynamic trait of the neutral Majorana particles, and thus lead to a dynamic understanding of mixing.