Linux Cubed Series 2: Applications/Linux Cubed Series 2 - Applications.iso/math/gle-3.000/gle-3/gle/lib/feyn.doc

Text File | 1995-03-08 | 12KB | 269 lines

       feyn.gle - a package for drawing Feynman diagrams
                   A.Grozin

It is often necessary to produce publication quality Feynman diagrams.
I know at least 3 tools intended for this purpose. The LaTeX package
FEYNMAN by M.J.S.Levine [1] constructs diagrams from characters
available in LaTeX fonts. It is therefore not enough flexible: it
permits a few slopes of lines, photon wavelengths and amplitudes, etc.
It requires to write a rather lengthy source to produce a moderately
complex diagram. The package Axodraw by J.A.M.Vermaseren [2] is much
more flexible. It is intended for use in LaTeX documents which will be
translated to PostScript by dvips, and directly generates PostScript
source for diagrams. From my point of view, it still misses several
useful features; and it hardly allows one to produce graphics formats
other than PostScript. Finally, there is FEYNMAN application in the
Instant TeX package on NeXT. It has a nice graphical user interface,
though it is not always easy to select a desired element by mouse in a
complicated diagram. In addition to this, it is platform-specific.

Due to these reasons, I have written a package of procedures for
drawing Feynman diagrams in the gle programming language. This language
is sufficiently convenient for programming, though it misses several
important features (the absence of local variables and the limitation
on a number of global variables are two most striking examples). A gle
source for a diagram can be used to produce graphic files in various
formats, either directly or with straightforward conversions. Preview
is nearly instant, so that it is easy to tune parameters of a diagram
by trial and error. It is also easy to include various geometric
calculations with square roots, arctangents, etc. to a gle program
(this is difficult in TeX packages and impossible in the NeXT graphics
environment).

To use the package in your gle program, write the line
        include feyn.gle
near the beginning. The package uses many variables beginning from F
for internal purposes. To avoid conflicts, don't use variables beginning
from this letter in your program. Please ignore error messages "Wrong
end" which may be produced occasionally. They are due to a bug in gle,
and don't influence a resulting diagram.

To draw a fermion (solid) line from (x1,y1) to (x2,y2), use
        amove x1 y1
    @Fermion x2 y2
After that, the pen is left at (x2,y2), so that
        @Fermion x3 y3
will draw line from (x2,y2) to (x3,y3). The line width can be
controlled by set lwidth.
        amove x1 y1
        @Fermion2 x2 y2 x3 y3
draws an arc from (x1,y1) via (x2,y2) to (x3,y3). For such an arc to be
uniquely defined, all three points must be different from each other.
In order to draw a complete circle, you should call Fermion2 twice.

Procedures for other kinds of lines are similar to the ones considered
above: they can draw a straight line from the current point to a given
point (x,y), or an arc from the current point via (x2,y2) to (x3,y3).
They leave the pen at the end point of the line. The call
        @Double x y
draws a double line from the current point to (x,y). The half-distance
between lines is determined by the variable DoubleA. The call
        @Dash x y
draws a dashed line to (x,y). The period of the dashed line is DashL,
and its fraction DashF is filled. For example, if you want dashes to be
twice as long as empty spaces between then, you should set DashF = 2/3.

A photon line is drawn by
        @Photon x y
Its half-wavelength is PhotonL, and amplitude - PhotonA. If you want
the waves to be in the opposite side, just change the sign of PhotonA.
Sometimes you may want both the first half-wave and the last one to be,
say, to the left, while the line produced by Photon has an even number
of half-waves. In such a case, you can add an extra half-wave by
setting PhotonN = +1, or eliminate one half-wave by setting PhotonN =
-1. This variable is reset back to 0 after each call. The call
        @Zigzag x y
produces a zigzag line, often used for a vector boson. This procedure
is controlled by the same parameters PhotonL, PhotonA, PhotonN.

A gluon line is drawn by
        @Gluon x y
Its wavelength is twice PhotonL, and its amplitude is PhotonA (a gluon
line always contains an integer number of periods, and PhotonN is not
used). The shape of a gluon line is controlled by the winding
coefficient GluonW. Wiggles become narrower when you decrease GluonW
from its default value 1, and degenerate to edges at 1/pi; at GluonW =
0, a gluon line looks like a photon one. When you increase GluonW,
wiggles become wider, and touch each other at GluonW = 1.46529 (this is
1/(pi*sin(x)), where x is the root of x+cot(x)=3*pi/2); beyond this
value they overlap. You may often wish to change the sign of PhotonA
so that wiggles will be to the opposite side. For example, gluon loops
usually look better when wiggles are inside; if an arc curves to the
left, this would require a negative PhotonA.

You can put an arrow at the middle of the last drawn line of any kind
by the call
        @Arrow 0.5
Similarly, the calls
        @Arrow 1/3
    @Arrow 2/3
will produce two arrows, at 1/2 and 2/3 of the line length from the
beginning. The position of an arrow is that of its tip. The length of
arrow wings is ArrowL; if it's negative, the arrow will point in a
direction opposite to that of the line. Half-width of arrow is ArrowA.
The arrow can be displaced in the transverse direction by setting
ArrowD non-zero, but this is rarely needed. After drawing an arrow, the
pen will be positioned again at the end of the line, so that you can
draw another line from this point.

A separate arrow near the middle of the last drawn line may be drawn by
        @Mom 0.5
It is often used for indication of the momentum flowing through the
line. The arrow is at the transverse distance MomD from the line, and
has half-length MomL. ArrowL and ArrowA are used as parameters of the
arrow wings. You will often need to change the sign of MomD to draw an
arrow to the other side from the line. In order to get an arrow
pointing in the opposite direction, you need to change signs of both
MomL and ArrowL. A similar call
        @DMom 0.5
produces a double arrow (with half-distance between lines DoubleA).
Such arrows can be used, e.g., to indicate spin projections.

Probably, a better way to understand how to use feyn.gle is to look at
the file ftest.gle containing some examples. Send comments and bug reports
to [e-mail]

References
[1] M.J.S.Levine, Comp. Phys. Comm. 58 (1990) 181.
[2] J.A.M.Vermaseren. Comp. Phys. Comm. 83 (1994) 45.

                   Appendix

All procedures and variables exported by the package are described below.
Following the wise saying "Don't throw away debugging tools from your
program after debugging is complete, because it is not complete" I
retained a primitive debugging procedure; you can use it if something
goes wrong.

================================ Fermion =================================
@Fermion x y
draws fermion line from the current point to x,y

@Fermion2 x1 y1 x2 y2
draws fermion line along the arc from the current point via x1,y1 to x2,y2
==========================================================================

================================ Double ==================================
@Double x y
draws double line from the current point to x,y

@Double2 x1 y1 x2 y2
draws double line along the arc from the current point via x1,y1 to x2,y2

DoubleA (default 0.05)
half-distance between lines
==========================================================================

================================ Dashed ==================================
@Dash x y
draws dashed line from the current point to x,y

@Dash2 x1 y1 x2 y2
draws dashed line along the arc from the current point via x1,y1 to x2,y2

DashL (default 0.3)
period of the dashed line

DashF (default 0.5)
fraction of the period that is filled
==========================================================================

================================ Photon ==================================
@Photon x y
draws photon line from the current point to x,y

@Photon2 x1 y1 x2 y2
draws photon line along the arc from the current point via x1,y1 to x2,y2

PhotonL (default 0.1)
half-period of the photon line

PhotonA (default 0.1)
amplitude of the photon line. When positive, the first half-wave is to the
left, when negative - to the right.

PhotonN (default 0)
change of the number of half-periods as calculated from PhotonL. Set to 0
after each call.
==========================================================================

================================ Zigzag ==================================
@Zigzag x y
draws zigzag line from the current point to x,y

@Zigzag2 x1 y1 x2 y2
draws zigzag line along the arc from the current point via x1,y1 to x2,y2

PhotonL, PhotonA, and PhotonN are used
==========================================================================

================================ Gluon ===================================
@Gluon x y
draws gluon line from the current point to x,y

@Gluon2 x1 y1 x2 y2
draws gluon line along the arc from the current point via x1,y1 to x2,y2

PhotonL and PhotonA are used

GluonW (default 1)
winding coefficient. Wiggles are wider when it is increased and narrower
when it is decreased
==========================================================================

================================ Arrow ===================================
@Arrow f
draws arrow on the last line of any sort, at the fraction of length f
from the beginning

ArrowL (default 0.5)
length of the arrow wings. When negative, arrow points backwards

ArrowA (default 0.2)
half-width of the arrow

ArrowD (default 0, rarely needed)
transverse displacement of the arrow from the line. When positive - to the
left, when negative - to the right
==========================================================================

================================ Momentum ================================
@Mom f
draws an arrow for indication of momentum near the last line, at the
fraction of length f from the beginning

ArrowL and ArrowA are used

MomL (default 0.75)
half-length of the arrow

MomD (default 0.5)
transverse displacement of the arrow from the line. When positive - to the
left, when negative - to the right
==========================================================================

========================= Double momentum arrow ==========================
@DMom f
draws a double arrow near the last line, at the fraction of length f from
the beginning

DoubleA, MomL, MomD, ArrowL, and ArrowA are used
==========================================================================

================================ Debugging ===============================
@fdebug l "name" variable
primitive debugging tool. If Debug>=l then writes the name and the value
of the variable at DebugX,DebugY and increments DebugY by DebugD. If
@fdebug is used inside begin {translate|rotate|scale} ... end, its output
will be {translated|rotated|scaled}, and may be outside the screen.

Debug (default 0)
level of debugging output

DebugX (default 1)
DebugY (default 1)
initial coordinates for debugging output

DebugD (default 1)
y increment for debugging output. If positive, later output is higher
==========================================================================