Abstract
The formalism of bundle maps is developed, then applied to several situations of physical interest. The bundle isomorphisms are defined to be inhomogeneous gauge transformations. First, we examine the compatibility between local gauge invariance with respect to an internal symmetry and the minimal coupling of the free gauge field Lagrangian to spacetime. In both homogeneous and inhomogeneous cases, restrictions arise which limit the torsion of the spacetime covariant derivative when applied to the gauge potential. Second, we examine the group of diffeomorphisms as a spacetime symmetry in the local gauge theoretic approaches to general relativity and the Einstein–Cartan theory of gravity.
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