In classical physics, charged particles induce electric field ##\vec{E}_c## around them. How do we interpret this classical electric field ##\vec{E}## in quantum mechanics.(adsbygoogle = window.adsbygoogle || []).push({}); Is this just the vacuum expectation value ##\vec{E}_c=<0|\vec{E}|0>##?if so, it means ##<A>\neq 0##. This would lead to Lorentz violation. So I don't know what's going on.

Another thing, we always try to define quantum modes in vacuum (the state with minimum energy). For instance, Higgs field is defined in some arbitrary vacuum of the potential: ##\phi=v+h## where ##\phi##, ##v## and ##h## are the original scalar field, vev ##<\phi>## and the higgs field respectively.Do we always have to do in this way(define excitation in vacuum ?I know this is essential for fermions, and W/Z bosons in SM to get mass. But does this really make sense? this makes me wonder what is field on earth.

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# Classical and quantum electromagnetic field

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