Macroscopic approach to quantum optics

This paper investigates how an approach alternative to the canonical quanti zation schemes may be used to describe Quantum Optics phenomena. By utilizi ng the approach pioneered by Keldysh, we derive equations for the time depe ndent correlation functions of the quantized optical fields. These contain the coupling to matter in linear and nonlinar response functions which repl ace the material parameters of phenomenological macroscopic theories. We pr esent these results as alternatives to existing theoretical methods in Quan tum Optics. The paper presents die general formulation of the theory, deriv es the equations in some specific cases relating to non-linear optics, and solves some illustrative special cases. We regain known results but also so me additional terms deriving from the quantum fluctuations of the material media.