% Read in by FEYNMANDOC:  FEYNMANDOC3C.  Called by FD3C.COM
\section{Gluon Vertices}

\subsection{The Anatomy of a Gluon Vertex}

When a three-gluon vertex is drawn in the N, S, E or W directions
using the \ddrawvertex\ command, diagonal gluon lines are drawn in a
\bs REG style, while horizontal and vertical lines
are drawn in a \bs CENTRAL configuration.
When a three-gluon vertex is drawn in the NE, SW, SE or NW directions
using the \ddrawvertex\ command, diagonal gluon lines are drawn in a
\bs REG style, while horizontal and vertical lines
are drawn in a \bs CURLY configuration.
When preceded by a \bs flipvertex qualifier line one (and only line one)
is flipped to become 
\bs FLIPPED, \bs FLIPPEDCURLY or \bs FLIPPEDCENTRAL.
When a Four-gluon vertex is produced all of the lines will be either
\bs REG (if drawn in a slanted direction) or \bs CURLY (if in a N, S, E or W
direction).  When \bs flipvertex is employed {\em all} of the lines will be
flipped.

The format is:
\begin{verbatim}

\drawvertex\gluon[<direction of gluon one><number of gluons>]
       <(x,y), the co-ordinates of the beginning of the gluon one>
       [<number of loops in each gluon line>]

\end{verbatim}

Gluonic vertices may be drawn in any of the eight compass directions.
If {\bf bold} gluons are desired then \bs THICKLINES {\it or}
\bs thicklines may be used.
The following parameters are returned by \ddrawvertex\bs gluon:

\begin{verbatim}

\gluonfrontx,\gluonfronty:   The (x,y) co-ordinates of the front of the last line.
\gluonbackx,\gluonbacky:     The (x,y) co-ordinates of the back of the last line.
\gluonlengthx,\gluonlengthy: The (x,y) extent of the last line.
\gluoncount:                 The number of gluons printed thus far.
\pfrontx,\pfronty:           The (x,y) co-ords of the front of the last line.
\pmidx,\pmidy:               The (x,y) co-ords of the middle of the last line.
\pbackx,\pbacky:             The (x,y) co-ordinates of the back of the last line.
\plengthx,\plengthy:         The (x,y) extent of the line.
\vertexonex,\vertexoney:     The (x,y) co-ordinates of the back of line one.
\vertextwox,\vertextwoy:     The (x,y) co-ordinates of the back of line two.
\vertexthreex,\vertexthreey: The (x,y) co-ordinates of the back of line three.
\vertexfourx,\vertexfoury:   The (x,y) co-ordinates of the back of line four.
\vertexmidx,\vertexmidy:     The (x,y) co-ordinates of the middle of the vertex.
\vertexcount:                The number of vertices printed thus far.

\end{verbatim}

\subsection{Examples and Details}

We illustrate the effect of \bs flipvertex in on three-gluon vertices.
The co-ordinate numbering has been done to scale.
\vskip 0.2in

\begin{picture}(30000,40000)
\drawvertex\gluon[\E3](5000,30000)[3]
\put(-4000,22000){{\tt \bs drawvertex\bs gluon[\bs E3](0,30000)[3]}}
\flipvertex\drawvertex\gluon[\E3](30000,30000)[3]
\put(19000,22000)
{{\tt \bs flipvertex\bs drawvertex\bs gluon[\bs E3](30000,30000)[3]}}
\drawvertex\gluon[\NE3](5000,10000)[3]
\put(-5000,8000){{\tt \bs drawvertex\bs gluon[\bs NE3](5000,10000)[3]}}
\flipvertex\drawvertex\gluon[\NE3](30000,10000)[3]
\put(19000,8000)
{{\tt \bs flipvertex\bs drawvertex\bs gluon[\bs NE3](30000,10000)[3]}}
\end{picture}

The following example illustrates how repeated use of the four-gluon
vertex may be employed with great effect.  It also illustrates a great
shortcoming of using gluon vertices since this small example uses up
most of \LaTeX's standardly available internal memory.  For this reason
an \bs{\it include} statement was used (see \LaTeX\ manual).

\begin{verbatim}

\begin{picture}(30000,15000)
\drawvertex\gluon[\E 4](15000,0)[3]
\drawline\fermion[\SW\REG](\vertexonex,\vertexoney)[\vertextwoy]
\flipvertex\drawvertex\gluon[\E 4](\vertexthreex,\vertexthreey)[3]
\drawvertex\gluon[\N 4](\vertextwox,\vertextwoy)[3]
\flipvertex\drawvertex\gluon[\W 4](\vertextwox,\vertextwoy)[3]
\drawline\fermion[\NW\REG](\vertexthreex,\vertexthreey)[\fermionlength]
\drawline\fermion[\S\REG](\vertexthreex,\vertexthreey)[\vertexthreey]
\end{picture}

\end{verbatim}
giving: