I would describe it as "outdated". It is formally equivalent to the more modern, quantum field-based description, but I think people don't like the way it poses things conceptually.
@gravity_levity is the Dirac sea a conventional or controversial model of the vacuum?
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It's kind of interesting that in my field (electronic systems) the Dirac sea picture has a literally-correct equivalent, which comes down to filled electron orbitals at low energy.
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