Linear quantization in quantum electrodynamics? This is a continuation of this question. 
What would be an example of linear quantization used on quantum electrodynamics? I ask this because QED is a nonlinear theory.
 A: I guess this was prompted by one of my comments on this question.  The point I was making is that quantization, even of a system which is defined by a Lagrangian encapsulating a nonlinear set of equations of motion (such as in interacting QED) proceeds by defining a Hilbert space of states and operators on this space which evolve unitarily $$ |\Psi(t)\rangle = e^{-iHt}|\Psi(0)\rangle $$ As soon as you have this behaviour, you have a Schroedinger equation (just differentiate it to see).
So the linearity and presence of the Schroedinger equation is an integral part of the quantum picture.  That's all I was meaning in the comment in the linked question.
A: Quantization is done for the free theory, without interactions, and this free theory is linear. For a scalar boson, for instance, each composant like $\phi(\vec k,t)$ is an harmonic oscillator (so the equation for $\phi(\vec k,t)$ is a linear equation), and you know how to quantize an harmonic oscillator.
When you  calculate the transition amplitudes, you are going to use the interaction term (S-Matrix), but the propagators you are using (in Feynmann diagrams) are calculated from the free theory quantization.
So there is no "quantization of interacting theory".
