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In the Relativistic Quantum Geometry (RQG) formalism recently introduced, wasexplored the possibility that the variation of the tensor metric can be done ina Weylian integrable manifold using a geometric displacement, from a Riemannianto a Weylian integrable manifold, described by the dynamics of an auxiliarygeometrical scalar field $\theta$, in order that the Einstein tensor (and theEinstein equations) can be represented on a Weyl-like manifold. In thisframework we study jointly the dynamics of electromagnetic fields produced byquantum complex vector fields, which describes charges without charges. Wedemonstrate that complex fields act as a source of tetra-vector fields whichdescribe an extended Maxwell dynamics.

Charged and electromagnetic fields from relativistic quantum geometry