Since we know the gauge theory can be emergent from local tensor product Hilbert space of quantum many body systems, such as solid state or condensed matter, etc.

How do we understand the ghosts in quantum many body systems?

Namely the Faddeev Popov ghosts in terms of many body quantum systems (for examples, from the energy band theory of lattice models, then with interactions, to have emergent gauge fields, etc)

The ghosts are needed some time to deal with the gauge fixing or to identify the unwanted negative norm states, in the 2nd quantized language.

So what do they mean in the 1st quantized language in many body quantum systems?

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    $\begingroup$ I don't quite understand the question. Ghosts are fictitious variables we introduce because it makes quantization of gauge theories easier. They are not visible in the physical state of space (in the quantum view) or after reducing to the constraint surface (in the classical view). Why do you think they need to mean anything "in the 1st quantized language"? $\endgroup$
    – ACuriousMind
    Jul 26, 2018 at 17:09
  • $\begingroup$ maybe ghosts dont have counter part in the 1st quantized langauge. But why dont they have any counter part, since both quantizations are part of quantum theory? Or maybe the 2nd quantized is not strictly a rigorously defined quantum theory? $\endgroup$ Jul 26, 2018 at 19:10


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