       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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```

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