Fiber Bundles, Connections, General Relativity, and the Einstein-Cartan Theory - Part II

The formalism of tetrads and spin connections is presented, and with it, the Einstein-Cartan (E-C) equations are derived from the usual actions. It is shown how torsion vanishes in the case of pure gravity. Then, the equations in the presence of the Dirac and the Maxwell fields are derived. A possibility of choosing a locally inertial coordinate system in the presence of a totally antisymmetric torsion is proved. We discuss a conflict between torsion and the local gauge invariance of the electromagnetic field. Finally, we study Lorentz and Poincar, gauge invariance of general relativity and the E-C theory.