Gauge theory of a group of diffeomorphisms. III. The fiber bundle description

A new fiber bundle approach to the gauge theory of a group G that involves space���time symmetries as well as internal symmetries is presented. The ungauged group G is regarded as the group of left translations on a fiber bundle G(G/H,H), where H is a closed subgroup and G/H is space���time. The Yang���Mills potential is the pullback of the Maurer���Cartan form and the Yang���Mills fields are zero. More general diffeomorphisms on the bundle space are then identified as the appropriate gauged generalizations of the left translations, and the Yang���Mills potential is identified as the pullback of the dual of a certain kind of vielbein on the group manifold. The Yang���Mills fields include a torsion on space���time.