When an interacting many-electron system is under an intense microwave radiation, the effects of the radiation field on the electron correlation functions cannot be treated within the framework of the conventional linear response theory. Recently we developed a new powerful method to calculate the effects of the intense time-dependent electric field on the electron wave function and the electron response functions. The key ingredient in the theory is the canonical transformation of the second quantized field operators describing the electrons. We shall examine the theoretical structure of the transformation and possible applications. © 2006 American Institute of Physics.