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Projective Relativity: Present Status and Outlook

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We give a critical analysis of projective relativity theory. Examining Kaluza's own intention and the following development by Klein, Jordan, Pauli, Thiry, Ludwig and others, we conclude that projective relativity was abused in its own terms and much more in the case of newer higher dimensional Kaluza–Klein theories with non-Abelian gauge groups. Reviewing the projective formulation of the Jordan isomorphy theorem yields some hints how one can proceed in a different direction. We can interpret the condition \(\mathop R\limits^5 _{\mu \nu } = 0\) not as a field equation in a 5-dimensional Riemannian space, e.g. as vacuum Einstein-Hilbert equation, but can (or should) interpret it as a geometrical object, a null-quadric. Projective aspects of quantum (field) theory are discussed under this viewpoint.

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  1. Fachbereich Physik, Fach M678, Universität Konstanz, 78457, Konstanz, Germany

    Bertfried Fauser

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Fauser, B. Projective Relativity: Present Status and Outlook. General Relativity and Gravitation 33, 875–887 (2001). https://doi.org/10.1023/A:1010259908844

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