Unified theory of gravitation, electromagnetism, and the Yang-Mills field

The recent modification and extension of Einstein's nonsymmetric unified field theory for gravitation and electromagnetism is generalized to include the Yang-Mills field theory. The generalization consists in assuming that the components of the linear connection and of the fundamental tensor are not ordinary $c$ numbers but are matrices related to some unitary symmetry. As an example we consider the SU(2) case. The theory is applied to the gauge-covariant formulation of electrically and isotopically charged spin-½ field theories.