Projective Relativity: Present Status and Outlook

Details Projective Relativity: Present Status and Outlook Projective Relativity: Present Status and Outlook

2000-11-04

arxiv.org/abs/gr-qc/0011015v1

Gen.Rel.Grav. 33 (2001) 875-887

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages

Scientific paper

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. 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 R5_{\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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