\chapter[XCOLOR: Color factor in gauge theory]%
{XCOLOR: Calculation of the color factor in non-abelian gauge
field theories}
\label{XCOLOR}
\typeout{{XCOLOR: Calculation of the color factor in non-abelian gauge
field theories}}
{\footnotesize
\begin{center}
A. Kryukov \\
Institute for Nuclear Physics, Moscow State University \\
119899, Moscow, Russia \\[0.05in]
e--mail: kryukov@npi.msu.su
\end{center}
}
\ttindex{XCOLOR}
XCOLOR calculates the colour factor in non-abelian gauge field
theories. It provides two commands and two operators.
\noindent{\tt SUdim} integer\ttindex{SUdim}
Sets the order of the SU group. The default value is 3.
\noindent{\tt SpTT} expression\ttindex{SpTT}
Sets the normalisation coefficient A in the equation
$Sp(T_i T_j) = A \Delta(i,j)$. The default value is 1/2.
\noindent{\tt QG}(inQuark, outQuark, Gluon)\ttindex{QG}
Describes the quark-gluon vertex. The parameters may be any identifiers.
The first and second of then must be in- and out- quarks correspondingly.
Third one is a gluon.
\noindent{\tt G3}(Gluon1, Gluon2, Gluon3)\ttindex{G3}
Describes the three-gluon vertex. The parameters may be any identifiers.
The order of gluons must be clockwise.
In terms of QG and G3 operators one can input a diagram in ``color'' space as
a product of these operators. For example
\newpage
\begin{verbatim}
e1
---->---
/ \
/ \
| e2 |
v1*............*v2
| |
\ /
\ e3 /
----<---
\end{verbatim}
where \verb+--->---+ is a quark and \verb+.......+ is a gluon.
The related \REDUCE\ expression is {\tt QG(e3,e1,e2)*QG(e1,e3,e2)}.