Examples and Details

The different styles of photon are:

The different directions may be illustrated by the following file:

% EXAMPLE OF USING FEYNMAN TO DRAW PHOTON DIAGRAMS IN TEX.
\documentstyle [11pt]{article}
\input FEYNMAN
\begin {document}
\centerline{PHOTONBURST using FEYNMAN}
\vskip 0.75in
\hskip 1.2in
\begin{picture}(20000,20000)(-10000,-10000)
\put(0,0){\circle*{1500}}
\drawline\photon[\N\REG](0,0)[8]
\drawline\photon[\NE\CURLY](0,0)[8]
\drawline\photon[\E\REG](0,0)[8]
\drawline\photon[\SE\CURLY](0,0)[8]
\drawline\photon[\S\REG](0,0)[8]
\drawline\photon[\SW\CURLY](0,0)[8]
\drawline\photon[\W\REG](0,0)[8]
\drawline\photon[\NW\CURLY](0,0)[8]
\end{picture}
\end{document}

A number of points may be noted. The first is the additional argument in the statement. This sets the lower left-hand corner of the picture box to the co-ordinates (-10000,-10000) in centipoints. Thus far this has been omitted and this corner is assigned the default co-ordinate of (0,0). The next point is the use of circle*. This draws a disk centred at the specified spot of the demanded diameter. Only small disks can be thus drawn. Also note that all of the photons begin their curvature in a clockwise sense. Similarly the flipped versions begin in a counter-clockwise orientation. In passing, the centerline command may be used as an alternative to the L^ATEX centered environment.

The next example illustrates a case where it becomes useful to be able to draw an odd number of half-wiggles.

\documentstyle [12pt]{article}
\input FEYNMAN
\begin {document}
\bigphotons
\begin{picture}(10000,10000)(0,0)
\drawline\photon[\E\REG](0,0)[8]  % Even number of half-wiggles.
\drawline\fermion[\NW\REG](\photonfrontx,\photonfronty)[\photonlengthx]
    % Make the fermions the same length as the photon.
\drawline\fermion[\SW\REG](\photonfrontx,\photonfronty)[\photonlengthx]
\drawline\fermion[\NE\REG](\photonbackx,\photonbacky)[\photonlengthx]
\drawline\fermion[\SE\REG](\photonbackx,\photonbacky)[\photonlengthx]
\global\divide\fermionlength by 2  %  Halves \fermionlength
\drawline\photon[\E\REG](\pmidx,\pmidy)[9]  % Odd number of half-wiggles.
\drawline\fermion[\SW\REG](\photonbackx,\photonbacky)[\fermionlength]
    % Draws fermion at the halved value of \fermionlength...which is 
    % Half of the value of the previous fermions.
\drawline\fermion[\NE\REG](\photonbackx,\photonbacky)[\fermionlength]
\drawline\photon[\E\FLIPPED](\pbackx,\pbacky)[8]  % Even number of half-wiggles.
\drawline\fermion[\NW\REG](\photonfrontx,\photonfronty)[\photonlengthx]
    % Make the fermions the same length as the photon.
\drawline\fermion[\NE\REG](\photonbackx,\photonbacky)[\photonlengthx]
\drawline\fermion[\SE\REG](\photonbackx,\photonbacky)[\photonlengthx]
\end{picture}
\vskip 1in
\end{document}

The next thing we observe is how the photonlengthx was used to draw the fermions and photons to the same length. This technique could not be used to draw, say, gluons and photons to the same length. Because of the angle between the second (middle) photon line and the fermion legs to which it is attached it was desirable to draw both ends of the photon as `down-turning'. If the connecting photon had been drawn between the upper fermion lines then, instead of the middle photon being
\drawline\photon[\E\REG](\pmidx,\pmidy)[7] it would have been
\drawline\photon[\E\FLIPPED](\pmidx,\pmidy)[7].

The next new item is the ``globaldivide'' command. This will be further discussed in chapter four but its function here is obvious. We wish to draw a fermion line centered at the end of the middle photon's right (East) end. The easiest way to do this is to draw fermions of half of the desired length in opposite directions. To obtain this value we use the statement \global\divide\fermionlength by 2 which reduces the value of this variable by a factor of two. The divisor must be integral and the quotient will be rounded to an integer. See the section on information storage for how to record the value of fermionlength prior to halving it. This technique could just as easily been used if, instead of a fermion, we had had a photon or gluon (with an even number of loops or half-wiggles). In these case one of the two halves would have been flipped with respect to the other. Can you see why a scalar could not be drawn this way?

The final point is that the third (right-most) photon was drawn in a flipped configuration in order to give a left-right symmetry to the diagram. The user is encouraged to try the following exercises. Firstly draw the above but with an even number of wiggles in all three photons to see the difference. Secondly try to draw the picture where photons connect both the upper and lower fermion pairs, creating a loop. Finally try to rotate the diagram through 45^o.

Aside from bigphotons discussed above there is one other photonic feature which we will mention in passing. Photons may be drawn with stems on them. This is an advanced feature which will be discussed in chapter four and an example illustrating the difference between a stemmed and unstemmed line will suffice for the present:

Exercise: The following diagram has eight lines. Using duplicate it using only eight commands.