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Massive scalar field on the static de Sitter space.

A massive scalar field on the static de Sitter metric is considered. The infrared divergence is shown to be logarithmic in {ital m}{sup 2}+{zeta}{ital R} and consistent with a thermal relation between the static and the de Sitter-invariant vacua. Finally, the difference of the trace of the energy-momentum tensor between both vacua is evaluated in the flat-space limit.