[scotty79]

This article contains a very neat description of what is energy, momentum and spin and why they there. Energy is just a quantity that's preserved when shifting through time, momentum is a quantity preserved by shifting through space. And spin is a quantity preserved by rotation in space-time.

General relativity treats energy and momentum jointly so I guess basically energy-momentum is a quantity preserved in space-time translations and spin is a quantity preserved in space-time rotations. (in flat space-time, I think?)

I guess that's why those Poincare symmetries are rarely mentioned when talking about particles. They seem to come more from sheer geometry of space-time than anything else. Particle physicists are mainly interested in all other symmetries (because they were harder to figure out). It also must be bad feeling that while you are trying pull gravity into your framework, more than half of the symmetries that the objects you spent your career observing obey, come from general relativity not from your framework.