Spacetime metrics from gauge potentials
arXiv:1403.7054 · doi:10.3390/sym6020164
Abstract
I present an approach to gravity in which the spacetime metric is constructed from a non-Abelian gauge potential with values in the Lie algebra of the group U(2) (or the Lie algebra of quaternions). If the curvature of this potential vanishes, the metric reduces to a canonical curved background form reminiscent of the Friedmann S^3 cosmological metric.
8 pages. Contribution to the special "Symmetry" volume: Physics based on two-by-two matrices