Quite generally, three-point (and higher order) correlators are used to reveal the non-Gaussian (read: nonclassical) character of the fields, see for example Experimental characterization of a quantum many-body system via higher-order correlations (also on arXiv)

One topic where correlation functions of high order are routinely studied is quantum transport: if you measure the conductance (determined by the average current) you are measuring a one-point correlator, the shot noise of the current gives you a two-point correlator, and by measuring higher order correlators you can reconstruct the full probability distribution of the transferred charge, with useful information on the quantum statistics of carriers.

Quite generally, three-point (and higher order) correlators are used to reveal the non-Gaussian (read: nonclassical) character of the fields, see for example Experimental characterization of a quantum many-body system via higher-order correlations (also on arXiv).

One topic where correlation functions of high order are routinely studied is quantum transport: if you measure the conductance (determined by the average current) you are measuring a one-point correlator, the shot noise of the current gives you a two-point correlator, and by measuring higher order correlators you can reconstruct the full probability distribution of the transferred charge, with useful information on the quantum statistics of the quasiparticles that carry the charge.

Quite generally, three-point (and higher order) correlators are used to reveal the non-Gaussian (read: nonclassical) character of the fields. You might find it motivating and instructive to have a look at Experimental characterization of a quantum many-body system via higher-order correlations (also on arXiv)

Quite generally, three-point (and higher order) correlators are used to reveal the non-Gaussian (read: nonclassical) character of the fields, see for example Experimental characterization of a quantum many-body system via higher-order correlations (also on arXiv)

One topic where correlation functions of high order are routinely studied is quantum transport: if you measure the conductance (determined by the average current) you are measuring a one-point correlator, the shot noise of the current gives you a two-point correlator, and by measuring higher order correlators you can reconstruct the full probability distribution of the transferred charge, with useful information on the quantum statistics of carriers.