In this paper we first show that any coupled system consisting of a
gravitational plus a free electromagnetic field can be described geometrically
in the sense that both Maxwell equations and Einstein equation having as source
term the energy-momentum of the electromagnetic field can be derived from a
geometrical Lagrangian proportional to the scalar curvature R of a particular
kind of Riemann-Cartan spacetime structure, where those fields are identified
as geometrical objects of the structure. We show moreover that the contorsion
tensor of the particular Riemann-Cartan spacetime structure of our theory
encodes the same information as the one contained in Chern-Simons term that is
proportional to the spin density of the electromagnetic field. Next we show
that by adding to the geometrical Lagrangian a term describing the interaction
of a electromagnetic current with a general electromagnetic plus the
gravitational field and a term describing the matter carrier of the current we
get Maxwell equations with source term and Einstein equation having as source
term the sum of the energy-momentum tensors of the electromagnetic and matter
terms. Finally modeling by dust charged matter the carrier of the
electromagnetic current we get the Lorentz force equation. Moreover, we prove
that our theory is gauge invariant. We also briefly discuss our reasons for the
present enterprise.Comment: In this version some few misprints have been corrected and a remark
has changed place. Paper will appear in Advances in Applied Clifford Algebra