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 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 point correlators
(n\leq 4n≤4)
to exemplify the general statements.