  We show that in the presence of external fields for which either
$\dot{\vb{B}}^{\mathrm{ext}}\neq 0$ or $\nabla\times\vb{E}^{\mathrm{ext}}\neq
0$ it is not possible to derive the classical Maxwell equations from an action
with only one gauge field. We suggest that one possible solution is to consider
a second physical pseudo-vector gauge field $C$. The action for this theory is
originally motivated by the inclusion of magnetic monopoles. These particles
play no role in this work and our argument is only based in, that the violation
of the Bianchi identities, cannot be accounted at the action level with only
the standard gauge field. We give a particular example for a periodic rotating
external magnetic field. Our construction holds that at classical level both
the vector and pseudo-vector gauge fields $A$ and $C$ are regular. We compare
pseudo-photon with paraphoton (graviphoton) theories concluding that, besides
the mechanisms of gauge symmetry breaking already studied, the Bianchi
identities violation are a crucial difference between both theories. We also
show that, due to Dirac's quantization condition, at quantum field theory level
the effects due to pseudo-photons and photons can be distinguished by the
respective contributions to the magnetic moment of fermions and vacuum
polarization. These effects may be relevant in astrophysical environments,
namely close and inside neutron stars and magnetars. [Erratum: The construction
in this work must, at most, be considered as a conceptual system or toy model.
Are discussed systems where the results may have relevance.]
