Nonsymmetric gauge theory of gravitation

Abstract

In this paper we give a nonsymmetric unified field theory, i.e., a gravitational gauge theory in which we take the group U(3,1) \ensuremath{\bigotimes} SU(2) as the gauge group. The electromagnetic field and the Yang-Mills field are brought naturally into the geometric construction of the spacetime. According to this theory, the torsion, which is Hermitian antisymmetric and its every component is a 2\ifmmode\times\else\texttimes\fi{}2 complex matrix, exists in the spacetime. In the special case or limit case, the U(3,1) gravitational gauge theory, the Lorentz gravitational gauge theory, the Einstein-Moffat-Boal theory, the Einstein-Maxwell theory, and general relativity are included in our theory.