
  \CompHEP~ constructs a list of quantum fields according to 
the Table of particles described above. Besides of names enumerated
in this table  \CompHEP~   generates  auxiliary fields, 
for example, the Faddeev-Popov ghosts \cite{BD}. We use the name
 {\it ghost} for all of them.

  The ghost fields do not  correspond  to physical degrees of freedom,
but each of them has some real particle as a prototype. The names of ghost 
fields are  constructed by \CompHEP~  from  the prototype particle name  followed
by a suffix which specify a type of ghost. The particle name and 
the suffix are separated by the dot symbol. It is assumed that the ghost 
fields explicitly  appear in the vertices of interactions together with
real particle fields and  thus contribute to the  particle interaction.
Below we list \CompHEP~ ghost fields.

\paragraph{ Faddeev-Popov ghost and anti-ghost.}
They  are  generated for any gauge vector particle, in other words,
for those  particles which have the  mark {\it 'g'} in the {\it 'Aux'} column 
of the {\it Particles} Table described in the   previous section.
  The names of Faddeev-Popov ghosts and anti-ghosts  are constructed by means of suffixes {\it 'c'} 
and {\it 'C'} respectively.  For example,  {\it G.c, G.C} are  gluon
ghosts and   {\it W+.c, W+.C, W-.c, W-.C}  are W-boson ghosts.

The operation of  Hermitian  conjugation  transforms a  Faddeev-Popov ghost
to itself whereas an anti-ghost  is transformed to itself with the  opposite  
sign. Thus the rules of Hermitian
conjugation of gluon and W-boson ghosts are
\begin{eqnarray*}
(G.c)^+&=&G.c\\  
(G.C)^+&=&-G.C\\
 (\mbox{W+.c})^+&=& \mbox{W-.c} \\  
(\mbox{W+.C})^+&=&-\mbox{W-.C}
\end{eqnarray*}
Faddeev-Popov (anti)ghosts are scalar, anti-commutative  fields
\footnote{ The well-known spin-statistic relation is not valid for unphysical
fields.}.   The nonzero propagators for these fields are:
$$<0|T[\mbox{A+.c}(p_1), \; A.C(p_2)]|0> = <0|T[\mbox{A+.C}(p_1), \;
A.c(p_2)]|0>  = ScPr(p_1,p_2,M),$$
where  $M$ is a mass of the prototype particle. This equality of masses is
 a consequence of  the choice  of the t'Hooft-Feynman gauge.

The appearance of the  Faddeev-Popov ghosts in gauge theories can be
explained  in the following way. In the case of the t'Hooft-Feynman gauge
the quantum field of massless gauge particle has two unphysical 
components, because the  four-dimensional vector field 
describes a particle with two polarization states. The contributions of
Faddeev-Popov ghost and anti-ghost  compensate  the contribution of these 
unphysical polarizations.  In the case of massive  gauge boson  there are 
three physical polarizations and the compensation by means  of 
 Faddeev-Popov ghosts looks wrong from the viewpoint of naive arguments 
based on  counting  
degrees of freedom.  Indeed, in this case one additional 
{\it  Goldstone}  ghost appears \cite{BD}.


\paragraph{ Goldstone ghost.}

It is  generated for any  massive gauge vector particles.
  The name of this field is constructed by means of suffix {\it 'f'}.  
For example,  {\it W+.f, W-.f}  are the W-boson Goldstone ghosts.

This  ghost is scalar,  commutative,  and satisfies  the same  
conjugation rule as the prototype particle. For example, $(W+.f)^+= W-.f$.
The nonzero propagators for these fields are:

$$T[\mbox{A+.f}(p_1), \; A.f(p_2)]   = ScPr(p_1,p_2,M),$$
where  $M$ is a mass of the prototype particle. 

\paragraph{ Tensor ghost.}

  Whereas  the  Faddeev-Popov  and Goldstone ghosts are standard
elements of modern quantum field theory, the tensor ghost is an
original \CompHEP~  invention. This is an auxiliary field with a point-like
propagator which is used to construct  vertices with   
complicated color structure, for example, the  four-gluon vertex.

The tensor ghost is generated automatically for any vector particle with a
non-trivial SU(3) color group representation. Its name is constructed by
means of suffix {\it 't'}.
This  ghost is  commutative,  and satisfies  the same
conjugation rule as the prototype particles. It is  Lorentz-transformed 
like  a tensor field. The propagator is 
\begin{equation}
<0|T[\mbox{A+.t}^{m_1M_1}(p_1), \; A.t^{m_2M_2}(p_2)]|0> = \frac{1}{(2 \pi)^4i} \; 
\delta(p_1+p_2) \, g^{m_1m_2}\, g^{M_1M_2}\;.
\label{tensor_propagator}
\end{equation}