<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">% FEYNMANDOC2B:  PART B OF CHAPTER 2; PHOTONS CONTINUED.  \included by 
%                                                             FEYNMANDOC       
\begin{verbatim}
                                 \REG
                                 \FLIPPED
                                 \CURLY
                                 \FLIPPEDCURLY
                                 \FLAT
                                 \FLIPPEDFLAT
                                 \LONGPHOTON
                                 \FLIPPEDLONG
                                 
\end{verbatim}

The \bs REG and \bs FLIPPED styles are available in all orientations.
The \bs LONGPHOTON and \bs FLIPPEDLONG photons are only available in the
\bs N and \bs S directions.
The others are available only in the following directions:
\verb^\N, \S, \NE, \SE, \NW, \SW^.  The \bs thicklines option is only available
to photons drawn in the \verb^\NE, \SW, \SE ^and \verb^\NW^\ directions,
however \bs THICKLINES is also available in the \verb^\E^ and \verb^\W^ 
orientations and has the same effect.
Attempts to draw a combination other than these will result in an
error message on the screen and in the $&lt;$jobname$&gt;$.lis file.
These options will be illustrated in the next subsection.

The parameters returned by \ddrawline\bs photon are analogous
to those returned after drawing fermions and scalars. 
These are:
\begin{verbatim}

\photonfrontx,\photonfronty:       The (x,y) co-ordinates of the front of the line.
\photonbackx,\photonbacky:         The (x,y) co-ordinates of the back of the line.
\photonlengthx,\photonlengthy:     The (x,y) extent of the line.
\photoncount                       The number of photons printed thus far.
\particlefrontx,\particlefronty:   The (x,y) co-ords of the front of the line.
\particlemidx,\particlemidy:       The (x,y) co-ordinates of the middle of the line.
\particlebackx,\particlebacky:     The (x,y) co-ordinates of the back of the line.
\particlelengthx,\particlelengthy: The (x,y) extent of the line.

\end{verbatim}

\subsection{Examples and Details}

The different styles of photon are:
\vskip 0.5in % \hskip 0.4in
\begin{picture}(42000,10000)
\drawline\photon[\S\LONGPHOTON](0,8000)[6]   
\put(-3000,10000){{\tiny \bs LONGPHOTON}}
\drawline\photon[\S\FLIPPEDLONG](6000,8000)[6]   
\put(3300,10000){{\tiny \bs FLIPPEDLONG}}
\drawline\photon[\S\CURLY](12000,8000)[6]   
\put(10500,10000){{\tiny \bs CURLY}}
\drawline\photon[\S\FLIPPEDCURLY](18000,8000)[6]   
\put(15000,10000){{\tiny \bs FLIPPEDCURLY}}
\drawline\photon[\S\FLAT](24000,8000)[6]   
\put(23000,10000){{\tiny \bs FLAT}}
\drawline\photon[\S\FLIPPEDFLAT](30000,8000)[6]   
\put(27000,10000){{\tiny \bs FLIPPEDFLAT}}
\drawline\photon[\S\REG](36000,8000)[6]   
\put(35000,10000){{\tiny \bs REG}}
\drawline\photon[\S\FLIPPED](42000,8000)[6]   
\put(40000,10000){{\tiny \bs FLIPPED}}

\end{picture}
\vskip 0.3in
The different directions may be illustrated by the following file:

\begin{verbatim}

% 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}

\end{verbatim}
Which produces:

\centerline{PHOTONBURST using FEYNMAN}
\vskip 0.75in
\hskip 1.4in
\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}
\vskip 0.5in

A number of points may be noted.   The first is the additional argument in the
\bbeginpic\ statement.  This sets the lower left-hand corner of the
picture box to the co-ordinates \hbox{(-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 \bs 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
{\em clockwise} sense.   Similarly the \bs flipped versions begin in a 
counter-clockwise orientation.
In passing, the \bs centerline command may be used as an
alternative to the \LaTeX\ centered environment.

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

\begin{verbatim}

\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}

\end{verbatim}
Which draws:
\vskip -0.15in
\hskip 0.5in
\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
Let us analyse this.
The first new feature that we see is the ``\bs bigphotons''
statement.  This statement is only required when photons are going to
be drawn either in the \bs E or \bs W directions {\bf and}
the document size has been selected to be [12pt].  It is best to
include it automatically if any Feynman diagrams are to be drawn in a 
12pt document.  It should appear somewhere after the \bs input FEYNMAN
statement and before the first \verb@\drawline\photon[\E...@ or
\verb@\drawline\photon[\W...@ command.  This is the only instance when
it is used.

The next thing we observe is how the \bs 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\\
\verb@\drawline\photon[\E\REG](\pmidx,\pmidy)[7]@ it would have been\\
\verb@\drawline\photon[\E\FLIPPED](\pmidx,\pmidy)[7]@.

The next new item is the ``\bs global\bs divide'' 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
\verb@\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 \bs 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 {\em 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 
\bs 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$^\circ$.

Aside from \bs bigphotons discussed above there is one other photonic
feature which we will mention in passing.  Photons may be drawn with
{\it 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:

\begin{picture}(25000,10000)
\drawline\photon[\E\REG](0,7000)[6]
\advance \photonfrontx by -800
\put(\photonfrontx,2000){UNSTEMMED}
\drawline\fermion[\NW\REG](\pfrontx,\pfronty)[2000]
\drawline\fermion[\SW\REG](\pfrontx,\pfronty)[2000]
\drawline\fermion[\NE\REG](\photonbackx,\photonbacky)[2000]
\drawline\fermion[\SE\REG](\photonbackx,\photonbacky)[2000]
\stemmed\drawline\photon[\E\REG](13000,7000)[6]
\photonbacky=\pbacky   \photonbackx=\pbackx
\advance \photonfrontx by 400
\put(\photonfrontx,2000){STEMMED}
\drawline\fermion[\NW\REG](\pfrontx,\pfronty)[2000]
\drawline\fermion[\SW\REG](\pfrontx,\pfronty)[2000]
\drawline\fermion[\NE\REG](\photonbackx,\photonbacky)[2000]
\drawline\fermion[\SE\REG](\photonbackx,\photonbacky)[2000]
\end{picture}
\vskip 0.30in
Exercise:  The following diagram has eight lines.  Using \FEYNMAN\
duplicate it using only eight commands.
\vskip 0.25in

%\begin{picture}(20000,20000)
\hskip 1.5in
\begin{picture}(20000,15000)
\thicklines\drawline\photon[\N\FLIPPEDCURLY](3000,3000)[7]
\drawline\fermion[\NW\REG](\pbackx,\pbacky)[\photonlengthy]
\drawline\fermion[\E\REG](\fermionfrontx,\fermionfronty)[\fermionlength]
\drawline\fermion[\SW\REG](\photonfrontx,\photonfronty)[\photonlengthy]
\drawline\fermion[\E\REG](\photonfrontx,\photonfronty)[\photonlengthy]
\drawline\fermion[\N\REG](\pbackx,\pbacky)[\photonlengthy]
\drawline\photon[\SE\REG](\fermionfrontx,\fermionfronty)[7]
\drawline\photon[\NE\FLIPPED](\fermionbackx,\fermionbacky)[7]
\end{picture}
\newpage
</pre></body></html>