Galilei, Poincare and conformal symmetry

[Heirot]

Reading this article: http://arxiv.org/abs/math-ph/0102011 made me wonder:

1.) So, it appears that Galilean transformations are not the most general symmetry transformations of nonrelativistic mechanics. Fine.
2.) The article states that the two additional symmetries are the nonrelativistic limit of conformal symmetries. But! Isn't it true that conformal symmetry is a symmetry of (and only of!) massless particles? Therefore it shouldn't have a nonrelativistic limit.
3.) So, either conformal symmetry lacks two parameters or I don't see how the nonrelativistic limit works. Where do the 3 leftover symmetries die out in the nonrelativistic limit?

[bcrowell]

1.) So, it appears that Galilean transformations are not the most general symmetry transformations of nonrelativistic mechanics.
I don't think that's quite what it says. It says that they are not the most general symmetry transformations of of a noninteracting point particle in nonrelativistic mechanics. The group they're talking about includes dilations, which are not a symmetry of Newtonian mechanics.

[Rocky Raccoon]

Doesn't the dilation symmetry correspond also only to massless particles?

[bcrowell]

Doesn't the dilation symmetry correspond also only to massless particles?

If they're noninteracting, then I guess there's no way even to measure their mass.