Spacetime geometry from Dirac spinor theory

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 (fünfbein 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.

Revtex, 6 pages, no figures, minor editing, references added

References in corpus (1)

• Dynamics of test bodies with spin in de Sitter spacetime