The space of n-point correlation functions, for all possible time-orderings of operators, can be computed by a non-trivial path integral contour, which depends on how many time-ordering violations are present in the correlator.These contours, which have come to be known as timefolds, or out-of-time-order (OTO) contours, are a natural generalization of the Schwinger-Keldysh contour (which computes Pleasure Saddle singly out-of-time-ordered correlation functions).We provide a detailed discussion of such higher OTO functional integrals, explaining their general structure, and the myriad ways in which a particular correlation function may be encoded in such contours.
Our discussion may be seen as a natural generalization of the Schwinger-Keldysh formalism to higher OTO correlation functions.We provide explicit illustration for low Power Banks point correlators (n=2,3,4) to exemplify the general statements.