  To obtain a generalized wave equation for a field in general covariant form,
one must define covariant differentiation of a generalized wave function
describing particles with arbitrary spin. Gel'fand and Iaglom, Dirac, and Fierz
and Pauli have studied the generalized wave equation in the special theory of
relativity. In this paper, the Gel'fand-Iaglom field equation was generalized
to the curved space based on the veilbein framework. The general covariant
field equations for arbitrary spin were obtained. More importantly, in this
work, we introduced the gauge covariant derivative with the local Lorentz
transformation, which is the foundation for a gauge theory of gravitation.
