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

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SUMMARY

Faddeev-Popov ghosts are not classified as fermionic fields due to their scalar nature under Lorentz transformations, leading to a violation of the spin-statistics theorem. These ghost fields are essential for eliminating unphysical polarizations in gauge theories, specifically in the context of gluon fields, which possess four components but only two physical transverse polarizations. The mathematical treatment of ghost fields involves the exponentiation of the Faddeev-Popov determinant using Grassmann numbers, allowing for the cancellation of contributions from unphysical polarizations.

PREREQUISITES
  • Understanding of gauge theories and their components
  • Familiarity with Faddeev-Popov procedure
  • Knowledge of Grassmann numbers and their properties
  • Basic principles of Lorentz transformations
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  • Study the Faddeev-Popov procedure in detail
  • Learn about the role of ghost fields in quantum field theory
  • Explore the implications of the spin-statistics theorem
  • Investigate the mathematical framework of Grassmann algebra
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The discussion is beneficial for theoretical physicists, quantum field theorists, and students studying advanced topics in gauge theories and field theory. It provides insights into the role of ghost fields in maintaining the consistency of gauge theories.

ndung200790
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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.
 
Physics news on Phys.org
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
 
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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