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 ---------------------------------------------------------------- Dept of Physics & Astronomy http://www.hep.man.ac.uk/u/jmonk Schuster Laboratory jmonk at hep.man.ac.uk University of Manchester Tel: Oxford Road U.K. (+44) (0)161 275 4226 Manchester U.S. (+01) (1)630 840 8321 M13 9PL ----------------------------------------------------------------