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

From: Bob McElrath
Subject: Re: [Axiom-developer] Re: FeynCalc -> MAXIMA
Date: Wed, 19 May 2004 09:16:52 -0700
User-agent: Mutt/

Bertfried Fauser address@hidden wrote:
> On Wed, 19 May 2004, Bob McElrath wrote:
> Dear Bob,
>       thank you for your explanation. Are there Hopf algebra methods and
> recently made advances also implemented in FeynCalc? The package Rafal and
> I developed, benefitted is speed and conceptual design cery much from Hopf
> algebraic techniques.

I do not know...

>       From a technical point of view, its algorithmically more sound to
> try to work in the Epstein-Glaser (etc pp) framework and *not* in the
> momentum (Feynman graph) picture, since the physical process is split up
> in an infinite series of integrals to be evaluated. AFAIK Hopf algebraic
> techniques seem to be the only way to come up with concise _and_
> algorithmically effective solutions.

Interesting, I will look into this.  I know only the feynman graph
picture, and have not even carried out very many loop calculations.

>       I am off for three weeks, and will look into FeynCalc, I can
> imagine to help withits portation to AXIOM though for several personal
> reasons. If you are interested in the things I have in mind, you may
> consider the recent JPysA article on Quantum fieldtheory and Hopf algebra
> cohomology, by Brouder,BF,Frabetti and Oeckl. Many of the calculations
> there were checked by the above mentioned package, though it was _not_
> designed for that purpose.

I am rather toward the user-of-FeynCalc side rather than the
invent-new-field-theoretic-techniques side.  If your Hopf algebra
methods are more efficent then I'm very interested...

I think the future of mathematics is for experts (such as yourself)
implementing and maintaining their favorite piece of math.  Clearly math
software can't evolve like normal Open Source because of the expertise
involved.  But it is critical for math to be open, especially as it
becomes more and more complicated, and more things become intractible to
do by hand.

FeynCalc involves a significant amount of "interface" for writing
lagrangians, etc that may not be appropriate for literal translation,
due to language differences.  It may be worth thinking hard about a
re-implementation of the functionality rather than a direct port.

> > The "algorithms" are documented in QFT textbooks such as Peskin &
> > Schroeder
> Would you really make this a claim? I still think, that without expert
> knowledge one cannot derive even simple results out of these sources...

I agree.

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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