Particles can be seen as "Unitary irreducible representations of the Poincare' group" using the Casimir of the representations: $m$ and $j$. Now, is it possible to generalize this procedure in order to classify all the "Unitary irreducible representations of the Diffeomorphism group"? If it's possible, does this give a generalization of the concept of particle? In both cases the group is acting on the space-time.
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1$\begingroup$ Nay, one cannot construct a notion of particles in general non-stationary spacetimes. Check out "Quantum Field Theory in Curved Spacetime, etc" by Robert Wald. $\endgroup$– ClassicStyleCommented Jan 6, 2017 at 2:28
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