We construct a quantum theory of light in nonlinear dielectric media with dispersion and absorption. We employ a mesoscopic model for the light-matter interaction that includes a fourth-order nonlinearity in the material response. Quantization is performed by constructing an effective action in a path-integral formalism by integrating out matter and bath degrees of freedom. We show how a nonlinear response function associated with Kerr nonlinearity is obtained through the model, and after full field quantization, we derive the Feynman rules from this theory.

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• Nonlinear optics
• Quantum optics
• Effective field theory
• Feynman diagrams
• Linear response theory
• Path-integral methods