MathGroup Archive 2002

[Date Index] [Thread Index] [Author Index]

Search the Archive

Multidimensional numerical integration problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg38506] Multidimensional numerical integration problem
  • From: "Andi Tröster" <troester at ap.univie.ac.at>
  • Date: Fri, 20 Dec 2002 04:27:42 -0500 (EST)
  • Organization: Vienna University, Austria
  • Sender: owner-wri-mathgroup at wolfram.com

hi,

i appologize in advance if the following sounds a little naive;
however, I have tried very hard to find a solution to
the following problem, without success, and I would appreciate
any hint towords a solution gladly:

i need to evaluate two mutidimensional integrals of the following form
as functions of a parameter m: (i give their form in TeX style to
make the problem more clear, and since a direct mathematica code
would not be useful anyway):

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

$$
I_1(m):=\int_{|p|<1} d^3p \int_{|q|<1} d^3q \int_{|r|<1} d^3r
\delta^3(p+q+r)
1/(p^2+m) 1/(q^2+m) 1/(r^2+m)
$$

$$
I_2(m):=\int_{|p|<1} d^3p\int_{|q|<1} d^3q\int_{|r|<1} d^3r
\delta^3(p+q+r+s)
1/(p^2+m) 1/(q^2+m) 1/(r^2+m) 1/(s^2+m)
$$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%`%%%

The dirac delta functions can of course be used to eliminate on of
the tree-dimensional integrals, in which case one is left with a
6 - and a 9-dimensional integral, respectively.

(To physicists: These integrals coorespond to certain Feynman diagrams in a
threedimensional
theory with mass m evaluated using a momentum cutoff at modulus 1)

I have tried various analytical simplifications  (like i.e. Schwinger
parametrization,
variable substitutions, partial integration etc.)
but I cannot come up with any form that allows a numerical evaluation for
m small, which is the case I am interested in.

Any ideas?

regards,

Andy




  • Prev by Date: Cox partial likelihood function, how to solve?
  • Next by Date: MathGL3.1 beta
  • Previous by thread: Re: Cox partial likelihood function, how to solve?
  • Next by thread: MathGL3.1 beta