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MathGroup Archive 2000

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Re: more wrong integrals

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24517] Re: more wrong integrals
  • From: Hendrik van Hees <h.vanhees at gsi.de>
  • Date: Mon, 24 Jul 2000 03:04:01 -0400 (EDT)
  • References: <8l685l$s8l@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

It seems indeed that Mathematica 4.0's Integrate has a lot of
shortcomings and as shown here some serious bugs. I don't know wether
Wolfram Research is really  caring about this Newsgroup. On my opinion
these are really bugs and should be corrected free of charge for all
users of Mathematica 4.0, for instance through downloadable bug fixes
from Wolfram's ftp-servers.

Some time ago I mentioned some problems concerning (relatively simple)
integrals which are typical for radiation correction calculations
("Feynman diagrams") in high energy particle physics. 

For the experts: I calculated simple one-loop integrals with dimensional
regularisation (by hand of course) and let Mathematica do the remaining
finite integrals over the Feynman parameter(s). The problem with these
integrals is that Mathematica gets out in principle the correct result
but does not care about the assumptions made for the parameters of the
integral. Especially putting the external momenta to the euclidean
region does not ensure the reality of the calculated diagrams which is
due to the wrong choice of the Riemann sheet. The only way out is to use
Mathematica only for finding the indefinite integral then setting by
hand the functions to the right sheets (there is a nice table about the
definition of the built in functions concerning the branch cuts and so
on somewhere in MathSource).

Concerning your two examples Mathematica 3.0 is better than 4.0 because
it states correctly that these integrals are not convergent.

-- 
Hendrik van Hees		Phone:  ++49 6159 71-2751
c/o GSI-Darmstadt SB3 3.183	Fax:    ++49 6159 71-2990
Planckstr. 1			mailto:h.vanhees at gsi.de
D-64291 Darmstadt		http://theory.gsi.de/~vanhees/index.html


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