Feynman Diagrams and the Sinc Function Representation
Richard Easther, Gerald Guralnik and Stephen Hahn
The Sinc function representation is a novel approach to the numerical
evalutation of Feynman integrals. It was introduced in our paper Fast
Evaluation of Feynman Diagrams, and in The Sinc
Function Representation and Three-Loop Master Diagrams we used it
to evalaute the master diagrams, whose analytic properties are
described by Broadhurst.
To illustrate how the method works in practice (and to help anyone
planning to use the Sinc function representation for their own
calculations) we are providing the codes we used to perform the
calculations described in our papers.
However, please take note of the following points:
- Anyone who wants to use, copy or redistribute these codes is free
to do so, but please mention us when (and if) you do. The code is
copyrighted, and if you want to distribute a modified version, please
check with us first.
- These is prototypes, not finished products, and we can see a
number of possible improvements. Furthermore, the parameter values are
included directly in the code itself, rather than being input by the
user. Thus to change the "input" you need to edit the source and
recompile (or add a couple of lines of code that lets you input
parameter values when the program runs).
- The code is written in Fortran 77, and while it is documented we
do not claim that it is pretty! In particular, the nested summations
could be tackled much more elegantly using recursive subroutines (in
Fortran 90), or in C/C++ which does not skip a beat when a procedure
- Declarations for common blocks (and their associated variables)
are inserted via an include 'header' command. This makes it easy to
keep the common blocks properly aligned, but it also means that each
subroutine ``sees'' more variables than it actually uses. If you were
careless, this could cause problems.
- The codes definitely works on a Sun Ultrasparc II (using versions
4.2 and 5.0 of the Sun Fortran 77 compiler, to be truly precise). Your
mileage may vary. We compiled with "f77 -fast", which aggressively
optimizes the resulting binary.
- Some warnings (underflow errors, mainly) are generated as the
code runs. Ideally we would trap these explicitly, but they are not
doing any harm.
- If you have suggestions, comments or questions, send me email.
These programs were used to evaluate the diagrams discussed in the
Fast Evaluation of Feynman Diagrams.
You will also need the following header files (which must be edited
slightly, see the comments in the source). You have to save the files
with the appropriate names (header and headerint).
- This is the header for the Sinc function
calculations. Comment out the appropriate lines before compiling.
- This is headerint, used for the version of
the sunset code which interpolates the inner sum.
This program evaluates the Sinc function representation of the master
diagrams, described in The Sinc Function Representation and Three-Loop