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

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In summary, Faddeev ghost fields are not considered as a type of fermi fields, but as scalars under Lorentz transformation. This leads to a wrong relationship between spin and statistics. The purpose of ghost fields is to "kill" unphysical polarizations of the gauge fields, which have four components but only two are physical. This is achieved through gauge fixing and the use of ghosts. Additionally, the exponentiation of the Faddeev-Popov determinant is only possible with Grassman numbers. While ghost and tachyon fields cannot be directly coupled to ordinary matter, they can act as intermediate states between gauge fields. This is because coupling them directly would have catastrophic consequences, as mentioned by the teacher of classical field
  • #1
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.
 
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  • #2
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
 
  • #3
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?
 

1. Why are Faddeev-Popov ghosts called "ghosts"?

Faddeev-Popov ghosts are called "ghosts" because they are not physical particles, but rather mathematical constructs used in certain quantum field theories. They are called "ghosts" because they have unusual properties that make them appear "ghost-like" compared to other particles.

2. What is the purpose of Faddeev-Popov ghosts in quantum field theory?

Faddeev-Popov ghosts are introduced in quantum field theory to cancel out certain unphysical degrees of freedom in the calculations. This is necessary in order to obtain meaningful and accurate results from the theory.

3. How do Faddeev-Popov ghosts help with gauge fixing?

In quantum field theory, gauge fixing is the process of choosing a specific gauge (a particular mathematical representation) for a given physical system. Faddeev-Popov ghosts help with this process by providing a way to remove unphysical degrees of freedom that would otherwise complicate the calculations.

4. Can Faddeev-Popov ghosts be observed or detected in experiments?

No, Faddeev-Popov ghosts are purely mathematical constructs and cannot be observed or detected in experiments. They are used as a tool in theoretical calculations, but do not have any physical manifestation.

5. Why are Faddeev-Popov ghosts necessary in some quantum field theories but not others?

Faddeev-Popov ghosts are necessary in certain quantum field theories, such as those involving gauge theories, because these theories have unphysical degrees of freedom that need to be accounted for. In other theories, such as those without gauge symmetry, these ghosts are not necessary. It depends on the specific mathematical structure of the theory.

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