  In this paper we provide an alternative method to compute correlation
functions in the in-in formalism, with a modified set of Feynman rules to
compute loop corrections. The diagrammatic expansion is based on an iterative
solution of the equation of motion for the quantum operators with only retarded
propagators, which makes each diagram intrinsically local (whereas in the
standard case locality is the result of several cancellations) and endowed with
a straightforward physical interpretation. While the final result is strictly
equivalent, as a bonus the formulation presented here also contains less graphs
than other diagrammatic approaches to in-in correlation functions. Our method
is particularly suitable for applications to cosmology.
