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Classification of outoftimeorder correlators
by Felix M. Haehl, R. Loganayagam, Prithvi Narayan, Mukund Rangamani
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Submission summary
Authors (as Contributors):  Mukund Rangamani 
Submission information  

Arxiv Link:  https://arxiv.org/abs/1701.02820v4 (pdf) 
Date accepted:  20181219 
Date submitted:  20181211 01:00 
Submitted by:  Rangamani, Mukund 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
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.
Published as SciPost Phys. 6, 001 (2019)
Author comments upon resubmission
List of changes
The following changes have been made in the new version of the manuscript to incorporate the suggestions of the referee. The numbering refers to the referee's comments at the end of their report.
Re 1) We have moved some of the very mathematical details from three different parts of the paper to a new appendix (C). We also put boxes around some of the important results in the main text to highlight the essential points. We left the derivation of Eq. (5.20) in the main text since it is mostly about building intuition for the contours rather than complicated mathematics (we did, however, put a suggestion to skip to the main result, on page 33 before the derivation starts).
We did not move the example section (section 7) to the beginning of the paper. We believe that sections 1 and 2 are quite pedagogical and provide an extensive introduction to the subject. Furthermore, the way section 7 is written is largely motivated by the results of the paper, so we feel it is more appropriate to have it at the end rather than at the beginning.
Re 2) We have now included a citation to this paper as suggested.
Re 3) We have now spelled out ``w.l.o.g.'' everywhere (however, please see https://en.wikipedia.org/wiki/Without_loss_of_generality where the usage is noted as standard).