Theory of matter in Weyl spacetime.

Abstract

Weyl's geometry of spacetime is reconsidered based on a novel geometric coupling between the Weyl vector and fermions. Starting from a manifestly Weyl-invariant action for the metric, Weyl field, spinors, and other fields, we introduce and define this coupling: the square root of the scalar Weyl curvature. An important consideration in this development is the reduction of the Weylian to an effective Riemannian structure for spacetime, without trivializing the role of the Weyl field. The aim of this reduction is to make contact with Einstein gravity for the metric sector of the theory. This is achieved by appealing to a dynamical-symmetry-breaking mechanism. The resulting spacetime is Riemannian, the Weyl field survives as a massive vector, and the geometric coupling to fermions decomposes into an admixture of vector and pseudovector couplings. Internal consistency of the field equations further narrows down the class of fermions which can couple to the Weyl vector: these can only be spinors of a fixed chirality. We tentatively identify them with the standard-model neutrinos. Analysis of couplings to other types of fields and particles indicates that the Weyl field is a form of dark matter.