Abstract
The elementary aspects of the spin-affine geometry borne by the Infeld-van der Waerden formalisms for classical general relativity are considered. It is explicitly shown that the symmetric parts of any admissible spin connexions behave covariantly under the action of the Weyl gauge group. The construction of a set of generalized covariant commutators provides a complete description of the corresponding curvature structures. The relevant computational procedures lead to a natural curvature splitting for each formalism which generally involves only the sum of purely gravitational and electromagnetic contributions. Under certain circumstances, the implementation of all commutators gives rise to a system of gauge-invariant wave equations for geometric photons and gravitons which carry prescribed index configurations.
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An erratum to this article can be found at http://dx.doi.org/10.1140/epjd/e2012-30278-x
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Cardoso, J.G. The Infeld-van der Waerden formalisms for general relativity. Czech J Phys 55, 401–462 (2005). https://doi.org/10.1007/s10582-005-0051-9
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DOI: https://doi.org/10.1007/s10582-005-0051-9