% Read in by FEYNMANDOC:  FEYNMANDOC4E.  Called by FD4E.COM
%\chapter{Advanced Features con't Links, Stems and Caps:  LINKS}
%
\section{Links, Stems and Caps}

In this section we discuss a number of important embellishments which may be
used to both simplify the construction of a diagram and beautify the results.

\subsection{Gluon Links}

Ideally one would like to draw identical lines (or vertices) following
one another and have them join seamlessly, as if a single line had been drawn.
For photons, scalars and fermions there is no difficulty in doing this.
For many styles of gluon this is likewise true.  For diagonally-drawn
gluons and those produced in the \verb@\CENTRAL@ style this is not the
case, as illustrated in section 2.10.2.  A similar problem ensues when
one wishes to attach a gluon to a vertex constructed from lines drawn in these
styles.

\subsubsection{Linking Lines}

The \bs gluonlink command is used between two \ddrawline\bs gluon statements
when the direction of the gluons is \verb@\NW, \NE, \SW @ or \verb@\SE@ or
when the gluons are both in a \verb@\CENTRAL@ or \verb@\FLIPPEDCENTRAL@ 
configuration.  It's effect is:
\begin{verbatim}

\begin{picture}(10000,5000)
% No \gluonlink:
\drawline\gluon[\NE\FLIPPED](0,0)[2]
\drawline\gluon[\NE\FLIPPED](\pbackx,\pbacky)[2]
%
% With \gluonlink:
\drawline\gluon[\NE\FLIPPED](5000,0)[2]\gluonlink
\drawline\gluon[\NE\FLIPPED](\pbackx,\pbacky)[2]
\end{picture}

\end{verbatim}
Note that the \bs gluonlink may also appear on a separate line or preceding the
second gluon.  There may be labelling statements interspersed but no other
lines may be joined.  The result is:


\begin{picture}(10000,5000)
% No \gluonlink:
\drawline\gluon[\NE\FLIPPED](0,0)[2]
\drawline\gluon[\NE\FLIPPED](\pbackx,\pbacky)[2]
%
% With \gluonlink:
\drawline\gluon[\NE\FLIPPED](5000,0)[2]\gluonlink
\drawline\gluon[\NE\FLIPPED](\pbackx,\pbacky)[2]
\end{picture}

Individually its effect is
\begin{verbatim}
\begin{picture}(5000,5000)
\drawline\gluon[\SE\REG](5000,0)[2]\gluonlink
\drawline\fermion[\N\REG](\gluonbackx,\gluonbacky)[1500]
\drawline\fermion[\SE\REG](\pbackx,\pbacky)[1500]
\end{picture}
\end{verbatim}
\begin{picture}(5000,5000)
\drawline\gluon[\SE\REG](0,5000)[2]\gluonlink
\drawline\fermion[\W\REG](\pbackx,\pbacky)[1500]
\drawline\fermion[\N\REG](\gluonbackx,\gluonbacky)[1500]
\end{picture}


\subsubsection{Linking Vertices}


When the number of loops is specified in a \ddrawvertex\ command,
every line radiating from the center has that number of loops.
A \bs gluonlink following the \ddrawvertex\ will pertain solely to the 
{\it last} line drawn.  In order to permit linkages to other or multiple
vertex lines the \bs {\it vertexlink} and
\bs {\it vertexlinks} commands are used.
Unlike \bs gluonlink, \bs vertexlink(s) {\it preceds} the \ddrawvertex\ 
statement.  The format is
\verb@\vertexlink@$n$, where $n$ is the line number of the vertex to be linked.
For a vertex drawn in a \verb@\S@ direction, line one is the first drawn,
\ie\ the \bs S line drawn {\it to} the centre (or if you prefer the \bs N
line coming out of the middle of the vertex).  The others are counted
clockwise around the midpoint \verb@(\vertexmidx,\vertexmidy)@.
\verb@\vertexlinks@ is an abbreviation of  
\begin{verbatim}
\vertexlink1\vertexlink2\vertexlink3
\vertexlink1\vertexlink2\vertexlink3\vertexlink4
\end{verbatim}
for a three and four line vertex respectively.
For instance, when the line

\begin{verbatim}
\vertexlink2\vertexlink3\flipvertex\drawvertex\gluon[\NE 4](0,0)[3]
\end{verbatim}
is encountered a four-gluon vertex (four lines each with 3 loops)
is drawn in the \bs flipped configuration.  The tip of the southwestern arm
is at (0,0) and the northwestern and northeastern arms have links attached
(ending at \verb@vertextwox,y@ and \verb@vertexthreex,y@ respectively).
The only time that a \verb@\N, \S, \E or \W@ gluon vertex requires a link is 
for \bs vertexone when a three-gluon vertex is drawn.  Vertices are generally
linked to gluon lines but may also be linked together directly as in the
following example.
\vskip 0.75in

\hskip 1.25in
\begin{picture}(8000,12000)
\vertexlink3 \drawvertex\gluon[\SE 4](0,14500)[3]
\flipvertex\drawvertex\gluon[\SE 3](\vertexthreex,\vertexthreey)[2]
\flipvertex\drawvertex\gluon[\E 4](\vertextwox,\vertextwoy)[4]
\end{picture}

which was produced by the three statements
\begin{verbatim}

\begin{picture}(8000,12000)
\vertexlink3 \drawvertex\gluon[\SE 4](0,11500)[3]
\flipvertex\drawvertex\gluon[\SE 3](\vertexthreex,\vertexthreey)[2]
\flipvertex\drawvertex\gluon[\E 4](\vertextwox,\vertextwoy)[4]
\end{picture}

\end{verbatim}
Note that the \bs E four-gluon vertex requires no special links (since it is
drawn using \bs CURLY style gluons).
In parting note that links may be drawn both with \bs THINLINES and 
\bs THICKLINES and will not appear when used within phantom mode
(section 4.1.2).
