A complete expression for the third-order susceptibility (χ(3)) - Perturbative and diagrammatic approaches

The complete expression, including all 48 terms, for the third-order nonlinear susceptibility
\chi^{(3)}
is written down explicitly. The diagrammatic and perturbative approaches to its derivation are matched and compared. The use of nontime-ordered (one-sided) diagrams is discussed and shown to give incomplete results.