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In this paper, we compute the effective action of both a scalar field and aDirac spinor field in the global de Sitter space of any dimension $d$ using thein-/out-state formalism. We show that there is particle production in evendimensions for both scalar field and spinor field. The in-out vacuum amplitude$Z_{in/out}$ is divergent at late times. By using dimensional regularization,we extract the finite part of $\log Z_{in/out}$ for $d$ even and thelogarithmically divergent part of $\log Z_{in/out}$ for $d$ odd. We also findthat the regularized in-out vacuum amplitude equals the ratio of determinantsassociated with different quantizations in $AdS_d$ upon the identification ofcertain parameters in the two theories.

Scalar and Spinor Effective Actions in Global de Sitter