Mass generation mechanism for spin 1/2 fermions in Dirac--Yang--Mills model equations with a symplectic gauge symmetry

Abstract

In the Standard Model of electroweak interactions the fundamental fermions acquire masses by the Yukawa interaction with the (spin 0) Higgs field. In our model spin 1/2 fermions acquire masses by an interaction with (spin 1) gauge field with symplectic symmetry.In [2,3,4,5,8] we develop a new approach to field theory, which based on so called model equations of field theory. In this paper we introduce Dirac-Yang-Mills model equations for spin 1/2 fermions interacting with two gauge fields simultaneously. One field has a unitary gauge symmetry and another has a symplectic gauge symmetry. There is no fermion's mass (m) term in the model Dirac equation. But there is the term 3m 3 /16 in the right hand part of the Yang-Mills equations with symplectic gauge symmetry. Hence, the constant 3m 3 /16 can be considered as a constant (charge) describing the interaction of a fermion with the symplectic gauge field.