Geometry of in-in correlators

Abstract

We introduce a family of polytopes -- in-in zonotopes -- whose boundary structure organizes the contributions to scalar equal-time correlators in flat space computed via the in-in formalism. We provide explicit Minkowski sum and facet descriptions of these polytopes, and show that their boundaries factorize into products of graphical zonotopes and lower-dimensional in-in zonotopes, thereby mimicking the factorization structure of the correlators themselves. Evaluating their canonical forms at the origin -- equivalently, calculating the volume of the dual polytope -- reproduces the correlator. Finally, in a simple example, we show that the wavefunction decomposition of the correlator corresponds to a subdivision of the dual polytope.