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arXiv · 2402.11593

Spacetime geometry from Dirac spinor theory

Yuri N. Obukhov·G. E. Volovik
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Abstract

The quintet of Dirac $4\times 4$ matrices suggests that the fundamental dimension of the internal (spin) space is $n=5$, instead of the conventional dimension $n=4$. Then extending the usual $4\times 4$ tetrads (vierbein), gravity is described in terms of the 5-bein (f\"unfbein or five legs). We discuss the properties of the spacetime geometry induced from this 5-leg Dirac spinor theory, where the spin connection contains $10\times 4=40$ elements instead of 24 elements in the tetrad formulation of the general relativity theory.

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Yuri N. Obukhov, G. E. Volovik. 2024-02-18. Spacetime geometry from Dirac spinor theory. https://doi.org/10.1103/physrevd.109.064076

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