  We investigate the relation between the time-ordered vacuum correlation
functions for interacting real scalar fields in Minkowski spacetime and in the
Rindler wedge. The correlation functions are constructed perturbatively within
the in-in formalism, often employed in calculations in more general spacetimes.
We prove to all orders in perturbation theory that the time-ordered vacuum
correlation functions can be calculated in the in-in formalism with internal
vertices restricted to any Rindler wedge containing the external points. This
implies that the Minkowski in-in (or in-out) perturbative expansion of the
vacuum correlation functions is reproduced by the Rindler in-in perturbative
expansion of these correlators in a thermal state at the Unruh temperature.
