  We show that higher degree Dirac currents of twistor and Killing spinors
correspond to the hidden symmetries of the background spacetime which are
generalizations of conformal Killing and Killing vector fields respectively.
They are the generalizations of 1-form Dirac currents to higher degrees which
are used in constructing the bosonic supercharges in supergravity theories. In
the case of Killing spinors, we find that the equations satisfied by the higher
degree Dirac currents are related to Maxwell-like and Duffin-Kemmer-Petiau
equations. Correspondence between the Dirac currents and harmonic forms for
parallel and pure spinor cases is determined. We also analyze the supergravity
twistor and Killing spinor cases in 10 and 11-dimensional supergravity theories
and find that although different inner product classes induce different
involutions on spinors, the higher degree Dirac currents still correspond to
the hidden symmetries of the spacetime.
