Matter fields in spacetime with vector nonmetricity

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Abstract
A metric-affine generalization of the Riemannian geometry is considered. In the torsion-free case the only characteristic object indicating the deviation from the Riemannian spacetime is a non-metricity tensor. Spacetime geometry with a generalized Weyl vector non-metricity is proposed and characteristic types of this geometry are systematically studied. Lagrangians and associated equations of motion of spinor and electromagnetic fields on the background of the spacetime with vector non-metricity (SVN) are considered in detail. The one-loop approximation in quantizing the non-metricity (metron) and electromagnetic fields on the Minkowskian background is treated to estimate the renormalized metron constant.

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