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

[Bob McElrath]

Bertfried Fauser address@hidden 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
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

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