Classifications of quasiparticles

Different particles can be represented as different irreducible representations of Poincare group. Can we classify quasiparticles using irreducible representations of some group? Also, quasiparticles are low energy excitations of the system, and it is closely related to the ground states of the system, so I am wondering if there is any relations we can use to help us classify quasiparticles from ground state symmetry. Also, is the irreducible representation of some group argument can apply to those excitations of topological origin?

• What is your precise definition of "quasiparticles" here? Commented Jun 6, 2017 at 11:27
• @ACuriousMind Sticking to standard vocabulary, he means the like of holes in semi-conductor, phonons in solids, etc. Actually maybe not the latter as sometimes quasi-particle is restricted to fermions.
– user154997
Commented Jun 6, 2017 at 12:07
• @LucJ.Bourhis See, that always happens - someone asks about the classifications of quasiparticles (or solitions, or "topological excitations"), I ask for a precise definition so we know what we actually want to classify, and the response is a list of examples. You'll have to admit that a list of examples is not a definition. Commented Jun 6, 2017 at 12:09
• Fair enough, the concept is ill-defined. But it is not the OP being sloppy here, so asking for a definition is too stringent here. At best, we could ask for a set of examples.
– user154997
Commented Jun 6, 2017 at 12:18
• @ACuriousMind I agree with you on the lack of rigorous definition, but I'd like to try :-) Why not defining quasi-particle (QP) as the elementary excitations on top of a spontaneous symmetry broken ground state, and considered as a free gas. I'm not sure one needs to require mean-field approximation to make it more sound. In any case, one can now give a few examples: Bogoliubov-QP for U(1) gauge redundancy breaking in superconductor, Galilean relativity breaking for neutral QP in superfluid, phonon-QP for translation invariance breaking, magnons for rotation breaking of ferromagnetic systems.. Commented Jun 7, 2017 at 6:47