Ricci Linear Weyl/Maxwell Mutual Sourcing

Abstract

We elevate the field theoretical similarities between Maxwell and Weyl vector fields into a full local scale/gauge invariant Weyl/Maxwell mutual sourcing theory. In its preliminary form, and exclusively in four dimensions, the associated Lagrangian is dynamical scalar field free, hosts no fermion matter fields, and Holdom kinetic mixing is switched off. The mutual sourcing term is then necessarily spacetime curvature (not just metric) dependent, and inevitably Ricci linear, suggesting that a non-vanishing spacetime curvature can in principle induce an electromagnetic current. In its mature form, however, the Weyl/Maxwell mutual sourcing idea serendipitously constitutes a novel variant of the gravitational Weyl-Dirac (incorporating Brans-Dicke) theory. Counter intuitively, and again exclusively in four dimensions, the optional quartic scalar potential gets consistently replaced by a Higgs-like potential, such that the co-divergence of the Maxwell vector field resembles a conformal vacuum expectation value.