On one hand, Dirac equation is supposed to be the equation of a classical field that we quantise. On the other hand, I saw many stackexchange posts saying that the classical limit of the electron field is very tricky to compute /not well defined because of the Pauli exclusion principle. But then what does the Dirac equation describe if not the classical electron field?
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- What do you mean by the classical electron field "existing"? 2. The Dirac equation is an equation of motion of a classical field. What do you mean when you ask whether this is "the classical electron field", given that you seem to be aware that we do not usually think about electrons in terms of a field in the classical regime.
– ACuriousMind Apr 01 '22 at 11:36 -
@ACuriousMind If the Dirac equation describes "a classical field" but it's not the electron classical field, then what classical field does it describe? Does that classical field exist only on paper or can we actually observe it as the macroscopic limit of the quantum electron field? – Ryder Rude Apr 01 '22 at 11:41
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So what you want to ask is whether the Dirac equation, as the equation of a classical field, usefully models any real-world situation? – ACuriousMind Apr 01 '22 at 11:47
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@ACuriousMind Yeah.... Or is it just a mathematical tool to get the Langrangian and the path integral? – Ryder Rude Apr 01 '22 at 11:48