  It has been shown that, for all dimensions and signatures, the most general
first-order linear symmetry operators for the Dirac equation including
interaction with Maxwell field in curved background are given in terms of
Killing-Yano (KY) forms. As a general gauge invariant condition it is found
that among all KY-forms of the underlying (pseudo) Riemannian manifold, only
those which Clifford commute with the Maxwell field take part in the symmetry
operator. It is also proved that associated with each KY-form taking part in
the symmetry operator, one can define a quadratic function of velocities which
is a geodesic invariant as well as a constant of motion for the classical
trajectory. Some geometrical and physical implications of the existence of
KY-forms are also elucidated.
