The coupled einstein-weyl field equations with cosmological constant and role of two higgs phenomena in weyl’s gauge model coupled to a higgs field

Abstract

We study, un.der the full action of gauge invariancc including two Itiggs phenomena, Weyl’s gauge model coupled to a Higgs field. As a result, we obtain the coupled Einsteia- Weyl field equations with the cosmological constant, which are analogous to the Einstein-Maxwell equations apart from difficulties inherent to Weyl’s geometry. The vacuum solution of a Higgs field will be discussed in connection with a manifestly gaugc-invariant formulation of the Lagrangian density of gravitation. A generalized action which is a function of the gauge-invariant scalar curvature is examined.