This lecture will begin to explore a generalization of General Relativity which has a closer resemblance to gauge theory than standard gravity. The generalization is obtained by demanding an additional local symmetry of the theory. In particular, just as we have the freedom to locally choose any orthonormal basis in the tangent space, we should have the freedom to choose a local orthonormal basis of the spinor space. Changing to another spinor basis induces an automorphism transformation of the Clifford algebra generators; thus we are lead to a gauge theory based on local automorphism invariance. This requires the introduction of the Clifford connection (the automorphism gauge field), as well as the drehbeins (akin to the vierbeins) as additional dynamical variables.
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