  The generalized Maxwell equations including an additional scalar field are
considered in the first-order formalism. The gauge invariance of the Lagrangian
and equations is broken resulting the appearance of a scalar field. We find the
canonical and symmetrical Belinfante energy-momentum tensors. It is shown that
the traces of the energy-momentum tensors are not equal to zero and the
dilatation symmetry is broken in the theory considered. The matrix Hamiltonian
form of equations is obtained after the exclusion of the nondynamical
components. The canonical quantization is performed and the propagator of the
fields is found in the first-order formalism.
