  The metric-affine Lagrangian of Ponomarev and Obukhov for the unified
gravitational and electromagnetic field is linear in the Ricci scalar and
quadratic in the tensor of homothetic curvature. We apply to this Lagrangian
the variational principle with the tetrad and spin connection as dynamical
variables and show that, in this approach, the field equations are the
Einstein-Maxwell equations if we relate the electromagnetic potential to the
trace of the spin connection. We also show that, as in the Ponomarev-Obukhov
formulation, the generally covariant Dirac Lagrangian gives rise to the
standard spinor source for the Einstein-Maxwell equations, while the spinor
field obeys the nonlinear Heisenberg-Ivanenko equation with the electromagnetic
coupling. We generalize that formulation to spinors with arbitrary electric
charges.
