Coframe geometry as a new unification scheme

The coframe field model is known as a viable model for gravity. The principle problem is an interpretation of six additional degrees of freedom. We construct a general family of connections which includes the connections of Levi-Civita and Weitzenb\"{o}ck. These two connections turn out to be the limiting cases of the family -- the Levi-Civita connection is invariant under arbitrary local Lorentz transformations while the Weitzenb\"{o}ck connection is invariant only under rigid Lorentz transformations. We propose to consider a middle case of a conditional invariant connection. We show that for a special choice of parameters, certain connections from the family are invariant when the infinitesimal field of transformations (antisymmetric tensor) satisfies the pair of vacuum Maxwell equations -- one for torsion and one for non-metricity. Such infinitesimal Lorentz transformations of the coframe field are proposed to be identified with the electromagnetic field components