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

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.