Broken Weyl invariance and the origin of mass

A massless Weyl-invariant dynamics of a scalar, a Dirac spinor, and electro mag netic fields is formulated in a Weyl space, W-4,W- allowing For conform al rescalings of the metric and of all fields with nontrivial Weyl weight t ogether with the associated transformations of the Weyl vector fields kappa (mu), representing the D(1) gauge fields, with D(1) denoting the dilatation group. To study the appearance of nonzero masses in the theory the Weyl sy mmetry is broken explicitly and the corresponding reduction of the Weyl spa ce W-4 to a pseudo-Riemannian space V-4 is investigated assuming the breaki ng to be determined by an expression involving the curvature scalar R of th e W-4 and the mass of the scalar, self-interacting field. Thereby also the spinor field acquires a mass proportional to the modulus Phi of the scaler field in a Higgs-type mechanism Formulated here in a Weyl-geometric setting with Phi providing a potential for the Weyl vector fields ii,. After the W eyl-symmetry breaking, one obtains generally covariant and U(1) gauge covar iant field equations coupled to the metric of the underlying V-4. This metr ic is determined by Einstein's equations, with a gravitational coupling con stant depending on Phi, coupled to the energy momentum tensors of the now m assive fields involved together with the (massless) radiation fields.