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Why does Limit sometimes just return what I input?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg44564] Why does Limit sometimes just return what I input?
*From*: jmonk <jmonk at hep.man.ac.uk>
*Date*: Fri, 14 Nov 2003 04:43:12 -0500 (EST)
*Sender*: owner-wri-mathgroup at wolfram.com
Hello,
I am trying to find the limit of some gamma matrix traces when a small
parameter \[Epsilon]->0. I am using the package Tracer.m and I define 4
lines:
Spur[l1, l2];
line11 = G[l1, p1, p3, G5, n, {Î½}, (p1 + k), {Î¼}];
line12 = G[l1, p1, p3, G5, n, {Î¼}, (p3 - k), {Î½}];
line21 = G[l2, p2, p4, G5, np, {Î»}, (p2 - k), {Î¼}];
line22 = G[l2, p2, p4, G5, np, {Î¼}, (p4 + k), {Î»}];
The vectors n and np are well defined by
OnShell[on,{n, xx_,\[Chi]1. xx + Î»\_1**\[Chi2p.xx]},
{np, xx_, lim[Î¶1 . xx + Î»\_\[Zeta]2p.¹*¶xx}];
with \[Chi]1, \[Chi]2p, Î¶1and\[Zeta]2p similarly defined. The momenta
p1...p4 also have their dot products defined. n and np depend on a small
parameter \[Epsilon], and it turns out that the highest order terms in the
lines line11...line22 are of order 1/\[Epsilon].
I want to take the limit e.g.
Limit[line11*\[Epsilon],\[Epsilon]->0,Direction->-1]
and then contract the 2 lines on the \[Mu] Lorentz index, but usually when
I try to take the limit it just returns the limit unevaluated.
Sometimes, however, it does return the limit. I can use the function
Residue to get the answer, but I want to know why Limit does not work.
The expressions for the lines are quite long - there are 338 terms, so I
wonder if it is too long for mathematica to cope with unless all of the
computer resources are available to it. I am running Mathematica 5.0 on
Mac Os X, G4 1Ghz 256 Mb.
The full script I have is too long to include, but I could forward it if
requested.
Any help and advice will be appreciated
Kind Regards
James
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Schuster Laboratory jmonk at hep.man.ac.uk
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Manchester U.S. (+01) (1)630 840 8321
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