Felix M. Haehl, R. Loganayagam, Prithvi Narayan, Mukund Rangamani
SciPost Phys. 6, 001 (2019) ·
published 7 January 2019

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The space of npoint correlation functions, for all possible timeorderings
of operators, can be computed by a nontrivial path integral contour, which
depends on how many timeordering violations are present in the correlator.
These contours, which have come to be known as timefolds, or outoftimeorder
(OTO) contours, are a natural generalization of the SchwingerKeldysh contour
(which computes singly outoftimeordered 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 SchwingerKeldysh formalism to higher OTO
correlation functions. We provide explicit illustration for low point
correlators (n=2,3,4) to exemplify the general statements.