Examples and Details

The following example illustrates that vertices need not only represent branchings but also crossed lines. 

\begin{picture}(22000,22000)
\drawline\fermion[\NE\REG](0,0)[6000]
\drawvertex\photon[\NE 4](\pbackx,\pbacky)[7]
\drawline\fermion[\N\REG](\vertexonex,\vertexoney)[\photonlengthx]
\drawline\fermion[\N\REG](\fermionbackx,\fermionbacky)[\plengthy]
\drawline\fermion[\NW\REG](\vertextwox,\vertextwoy)[6000]
\end{picture}
Producing
\begin{picture}(22000,22000) \drawline\fermion[\NE\REG](0,0)[6000] \drawvertex\p... ...lengthy] \drawline\fermion[\NW\REG](\vertextwox,\vertextwoy)[6000] \end{picture}
A couple of items may be noted. In order to draw the connecting fermion line we've drawn it in two stages. We know that photonlengthx will return the horizontal length of line four of the four-photon vertex. Since line one is the one radiating from the centre in the SW direction (since it was drawn to the centre of the vertex in the NE direction) we count around clockwise to the fourth line being in the SE direction. Since the picture is symmetric the `x' extent of line four is equal to the `y' extent of lines one and two. Therefore to connect the ends of lines one and two we need to draw a fermion of that length twice. In the second statement we use plengthy so that it is the same length as the previous line. If, instead, we'd wanted


\begin{picture}(12000,12000)(-10000,0) \drawline\fermion[\NE\REG](0,0)[6000] \TH... ...\flipvertex\drawvertex\photon[\SE 3](\vertexfourx,\vertexfoury)[4] \end{picture}
we'd have added 

\THICKLINES\flipvertex\drawvertex\photon[\NE 3](\vertexthreex,\vertexthreey)[4]
\flipvertex\drawvertex\photon[\SE 3](\vertexfourx,\vertexfoury)[4]
and put a \THICKLINES modifier before the first and a \THINLINES following it. Note how we had to use flipvertex in order to make the sets of vertices connect properly. In point of fact the above pictures are flawed since the two fermion-fermion-photon vertices are not symmetric. In this instance it would be more appropriate to draw two long photons instead of a vertex.

Photonic vertices may also be stemmed, as will be discussed in the next chapter (however see section 2.9 for an example of stemmed photons). Finally we point out, in the form of an exercise, that being able to produce photons with an odd number of half-wiggles again has its uses. Exercise: Draw the following using . How could you replace the fermion on the right by a scalar?
\begin{picture}(20000,12000)(0,-6000) \drawline\photon[\E\REG](4000,0)[7] \drawl... ...rawline\fermion[\SE\REG](\vertexthreex,\vertexthreey)[\vertextwoy] \end{picture}
Note that the diagonal fermion segments on the right have half of the length of the vertical segment.