  We consider quantum field theory with selfinteractions in various patches of
Minkowski and de Sitter space-times. Namely, in Minkowski space-time we
consider separately right (left) Rindler wedge, past wedge and future wedge. In
de Sitter space-time we consider expanding Poincare patch, static patch,
contracting Poincare patch and global de Sitter itself. In all cases we
restrict our considerations to the isometry invariant states leading to
maximally analytic propagators. We prove that loop corrections in right (left)
Rindler wedge, in the past wedge (of Minkowski space-time), in the static patch
and in the expanding Poincare patch (of de Sitter space-time) respect the
corresponding isometries of the corresponding symmetric space-times. All these
facts are related to the causality and analyticity properties of the
propagators for the states that we consider. At the same time in the future
wedge, in the contracting Poincare patch and in global de Sitter space-time
infrared effects violate the isometries.
