Formal properties of the third-order response. Section 1.5 contains a description of some of the formal mathematical properties of the second order susceptibility. For the present problem, you are to determine the analogous symmetry properties of the third-order susceptibility χ(3) . In your response, be sure to include the equations analogous to Eqs. (1.5.1), (1.5.2), (1.5.5), (1.5.6), (1.5.8), (1.5.9), and (1.5.19).
