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

Equivalence between the in-in perturbation theories for quantum fields in Minkowski spacetime and in the Rindler wedge