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We apply the covariant analytic mechanics with the differential forms to theDirac field and the gravity with the Dirac field. The covariant analyticmechanics treats space and time on an equal footing regarding the differentialforms as the basic variables. A significant feature of the covariant analyticmechanics is that the canonical equations, in addition to the Euler-Lagrangeequation, are not only manifestly general coordinate covariant but also gaugecovariant. Combining our study and the previous works (the scalar field, theabelian and non-abelian gauge fields and the gravity without the Dirac field),the applicability of the covariant analytic mechanics is checked for allfundamental fields. We study both the first and second order formalism of thegravitational field coupled with matters including the Dirac field. It issuggested that gravitation theories including higher order curvatures cannot betreated by the second order formalism in the covariant analytic mechanics.

Application of covariant analytic mechanics with differential forms to gravity with Dirac field