Why ghost fields(Faddeev-Popov ghosts) must be ''ghost''?

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Please teach me this:
Why can we not consider Faddeev ghost as a type of fermi fields,but consider them as a scalar under Lorentz transformation,therefore have wrong relation between spin and statistics?
Thank you very much for your kind helping.
 

tom.stoer

Science Advisor
5,759
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physicall: ghost fields must "kill" unhysical polarizations of the gauge fields; the gluon fields has four components, but only two polarizations are physical (transversal). Gauge fixing + ghosts cancel the contribution of the two unphysical polarizaton.

mathematically: exponentiating the Fadeev-Popov determinant is possible only with Grassman numbers
 
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I would add one question about ghost field: in one lecture, my teacher of classical field theory introduced ghost and tachyons saying that we can't couple them to ordinary matter because (quoting) "it would mean the destruction of the universe". So how is it that they couple as intermediate states between gauge fields?
 

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