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arXiv · 1701.02820

Classification of out-of-time-order correlators

Felix M. Haehl·R. Loganayagam·Prithvi Narayan·Mukund Rangamani
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Abstract

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=2,3,4) to exemplify the general statements.

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Felix M. Haehl, R. Loganayagam, Prithvi Narayan, Mukund Rangamani. 2017-01-11. Classification of out-of-time-order correlators. https://doi.org/10.21468/scipostphys.6.1.001

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