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The extension of the adiabatic regularization method to spin-$1/2$ fieldsrequires a self-consistent adiabatic expansion of the field modes. We providehere the details of such expansion, which differs from the WKB ansatz thatworks well for scalars, to firmly establish the generalization of the adiabaticrenormalization scheme to spin-$1/2$ fields. We focus on the computation ofparticle production in de Sitter spacetime and obtain an analytic expression ofthe renormalized stress-energy tensor for Dirac fermions.

Adiabatic regularization and particle creation for spin one-half fields