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In my understanding, where the value of a quantum field [i.e. a field with discrete values] is 0 it is said to be in the ground state, and where it is not 0 it is said to be an excitation. Why do we not use the same convention with non-quantum fields [i.e. fields where any real value is possible]. My only guess is that it is very rare for a non-quantum field is to be at exactly 0, so the terminology has no practical use outside of quantum fields.

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    $\begingroup$ Quantum fields are not "fields with discrete values". $\endgroup$
    – fqq
    Commented Feb 16, 2022 at 22:11
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    $\begingroup$ "In my understanding, where the value of a quantum field [i.e. a field with discrete values] is 0 it is said to be in the ground state, and where it is not 0 it is said to be an excitation." Every part of this sentence is wrong. Quantum fields do not have definite values, let alone discrete ones. For what an "excitation" of a quantum fields is, see e.g. physics.stackexchange.com/q/154391/50583, physics.stackexchange.com/q/127141/50583 and their linked questions. $\endgroup$
    – ACuriousMind
    Commented Feb 16, 2022 at 22:11

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