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Apr 14, 2019 at 14:34 comment added ACuriousMind @SRS Please do not use comments for follow-up questions. If you have a new question, ask a new question. Note that the electric field is a) not a scalar and b) not a "quantum field" (in the sense that the exp. value of its square would be related to a propagator) since the dynamical variable of the EM Lagrangian is the potential, not the field strength, so it has nothing to do with the variance of a scalar quantum field your question here asks about.
Apr 14, 2019 at 14:25 comment added SRS Ah... right. Do you have any idea about why the vacuum fluctuations of the electric field turns out to be finite in quantum optics but not in QFT? It seems that it is because that they find the vacuum fluctuation for a single mode? Here is the link of a 5 min video by Alain Aspect. youtube.com/watch?v=jXxW82L6os8 I am not sure why is the vacuum fluctuation of a single mode is experimentally meaningful @ACuriousMind
Apr 13, 2019 at 11:48 history answered ACuriousMind CC BY-SA 4.0