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MathGroup Archive 2003

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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, {ν}, (p1 + k), {μ}];
line12 = G[l1, p1, p3, G5, n, {μ}, (p3 - k), {ν}];
line21 = G[l2, p2, p4, G5, np, {λ}, (p2 - k), {μ}];
line22 = G[l2, p2, p4, G5, np, {μ}, (p4 + k), {λ}];

The vectors n and np are well defined by

OnShell[on,{n, xx_,\[Chi]1. xx + λ\_1**\[Chi2p.xx]},
	{np, xx_, lim[ζ1 . xx + λ\_\[Zeta]2p.¹*¶xx}];

with \[Chi]1, \[Chi]2p, ζ1and\[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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