Abstract
The starting point is a spinor affine space-time. At each point, two-component spinors and a basis in spinor space, called “spin frame,” are introduced. Spinor affine connections are assumed to exist, but their values need not be known. A metric tensor is not introduced. Global and local gauge transformations of spin frames are defined with GL(2) as the gauge group. Gauge potentials B μ are introduced and corresponding fields F μν are defined in analogy with the Yang-Mills case. Gravitational field equations are derived from an action principle. Incases of physical interest SL(2, C) is taken as the gauge group, instead of GL(2). In the special case of metric space-times the theory is identical with general relativity in the Newman-Penrose formalism. Linear combinations of B μ are generalized spin coefficients, and linear combinations of F μν are generalized Weyl and Ricci tensors and Ricci scalar. The present approach is compared with other formulations of gravitation as a gauge field.
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