Mathematical Physics


The Bianchi Identities in Weyl Space

Authors: William O. Straub

As far as the writer is aware, the Bianchi identities associated with a Weyl space have never been presented. That space was discovered by the noted German mathematical physicist Hermann Weyl in 1918, and represented the geometry underlying a tantalizing theory that appeared to successfully unify the gravitational and electromagnetic fields. One of theory’s problems involved one form of the Bianchi identities, which in Riemannian space are used to derive the divergenceless Einstein tensor. Such a derivation is generally not applicable in a non-Riemannian geometry like Weyl’s, in which the covariant derivative of the metric tensor is non-zero. But it turns out that such a derivation is not only possible but straightforward, with a result that hints at a fundamental relationship between Weyl’s geometry and electromagnetism.

Comments: 3 Pages. Fixed typo in Equation 4.3

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Submission history

[v1] 2015-08-05 14:54:01
[v2] 2016-07-29 17:09:32

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