Wave fields in Weyl spaces and conditions for the existence of a preferred pseudo-Riemannian structure

Abstract

Following an axiomatic formulation for general relativity, an equivalent class of pseudo-Riemannian manifolds is derived from the Lorentz conformal structure given by the sets of all possible light rays and all possible free falling objects, the latter set defining the affine geodesics. In particular the set of null geodesics defined by the Lorentz conformal structure characterize a Weyl space-time structure. \par It has been shown by one of the authors that when the classical trajectories of matter fields defined over the Weyl space-time are assumed to coincide with the geodesics of that space, then a set of Lorentzian space-times arise naturally. In the present paper the authors improve this result by use of fiber bundles and the WKB limit to derive the short wave limits to Dirac and Klein-Gordon fields.