Sketch of a Gauge Model of Gravity with SU(2) Symmetry in Minkowski space

Abstract

We propose a gauge model with the SU(2) symmetry, which describes a gravitational interaction of fundamental fermions (leptons and quarks) in the Minkowski space. In the Standard Model one uses a Dirac-Yang-Mills system of equations with U(2) gauge symmetry for electroweak interactions and with SU(3) gauge symmetry for QCD interactions. A key idea of the model is to use the Dirac-type equation (invented in 2002) instead of the standard Dirac equation. This Dirac-type equation has an additional SU(2) gauge symmetry. The Yang-Mills field, which corresponds to this SU(2) symmetry, we identify with the gravitational field of interacted fundamental fermions. Some elements of Clifford analysis are used in the model.