  From one point of view in the quantum theory of fields, free quantum fields
are uniquely determined, not by field equations, but by the transformations of
the field and the annihilation and creation operators from which the field is
constructed. One says that a free field equation merely records the fact that
some field components are superfluous. Here, free field equations that are
first order and covariant are derived so that the already determined field is
one solution. The unknowns are the vector matrices that combine with the known
gradient of the field to make an invariant equation: the scalar product of the
vector matrices and the gradient are proportional to the field. Thus these free
field equations are direct consequences of the transformation properties of the
annihilation and creation operators and the transformation properties of the
field.
