Re: [Axiom-developer] Re: FeynCalc -> MAXIMA

Greetings!

Bob McElrath <bob+maxima@mcelrath.org> writes:

> Bertfried Fauser [fauser@spock.physik.uni-konstanz.de] wrote:
> > 
> > Hi,
> > 
> > as fare as I understand the package (havn't though done much with it, so I
> > might be wrong), it is designed for very "practical" purpose (ie
> > phenomenology.) Many problems can be subsummarized in a larger frame of
> > mathematics. Given the type system of AXIOM, it would be, in my eyes, a
> > fraud to implement something like "Dirac matrixes" and trace rules, while
> > this is a closed structure in a *-autonomous category. However, I am still
> > not able myself to give AXIOM code for such a vast general thing.
> 
> The *purpose* of FeynCalc is to be a general purpose framework for doing
> quantum field theory calculations.  That is, dirac matrices, trace
> rules, Feynman rules from Lagrangians, representations for fields and
> the like.
> 
> It also contains code for doing one-loop integrals.  This same code
> exists in several places (I know of a fortan library "ff" and a Maple
> package "xloops" as well), and I can point to the papers if people
                                 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

I think this would be helpful.

Take care,


> desire.  But the loop code is only half of FeynCalc.
> 
> The actual algorithms are straightforward, but very tedious to
> calculate, so thus the results are collected into libraries like
> FeynCalc.  There are yet a handful of obstacles in dealing with
> divergences that have kept us from writing a fully automatic method of
> computing these loop integrals.  At one loop I think it can be fully
> automatic, but I do not think this is something a non-expert would want
> to tackle.
> 
> The "algorithms" are documented in QFT textbooks such as Peskin &
> Schroeder "An Introduction to Quantum Field Theory", Weinberg "Quantum
> Theory of Fields", etc.  This is a one-year graduate level physics
> course.  The decomposition of loop integrals into scalar integrals was
> done by Passarino and Veltman
>     http://dx.doi.org/10.1016/0550-3213(79)90234-7
> though these days it's not the only way...
> 
> Cheers,
> Bob McElrath [Univ. of California at Davis, Department of Physics]
>     
>     "A great many people think they are thinking when they are merely
>     rearranging their prejudices." -- William James
> 

-- 
Camm Maguire			     			camm@enhanced.com
==========================================================================
"The earth is but one country, and mankind its citizens."  --  Baha'u'llah