# When is quasiparticle same as elementary excitation, and when is not?

Can anyone shed light on the comparison between these two concepts?

• As it stands this is rather a broad question. The best course would be for you to read around the area a bit and come back to us with any specific questions. Dec 17, 2013 at 7:21
• See physics.stackexchange.com/questions/21954/… for an answer. Mar 28, 2014 at 1:56

Dictionary for this answer: Excitation = particle; collective excitation = quasi-particle.

Elementary particles are never quasi-particles, by definition of elementary. This does not mean that what now it is thought as an elementary particle could be a quasi-particle of entities to be discovered.

Elementary particles are those that correspond to irreducible representations of the Poincare group.

Quasi-particles require the existence of an external medium or fields, whereas elementary particles do not. For example, phonons require a solid or a fluid to exist (they are collective modes of the atomic lattice vibration), likewise pions require a quark-antiquark sea. These are not fundamental particles, in the sense that they need the existence of other particles. A closed notion is that of composite particle, for example a molecule is made of atoms which, in turn, are made of a nucleus plus electrons. The difference between quasi and composite particles lies in the fact that quasi-particle are though as collective excitations of many particles (usually of the order on the Avogadro number $\sim 10^{23}$, but there may be far fewer, but not tens), while composite particles are more like building blocks where each constituent may be an elementary particle—such as an electron— or another composite particle—such as an atom— (a molecule is usually made of a few or tens of atoms, an atom usually contains from a few to tens of electrons plus a nucleus). Nevertheless, the difference between both concepts is not sharp; for example, pions are somehow made of quarks and antiquarks, they actually are also collective modes (waves) on the quark-antiquark sea, being quasi-Goldstone bosons of the approximate chiral symmetry.

The difference between elementary and composite particles is tied to the human knowledge at the time. At a certain point, it was though that nuclei were elementary, after that people realized that there were in fact more fundamental constituents (protons and neutrons), and later on quarks and gluons were discovered.

• Thank you very much! Could you please explain more about the 'Mathematical answer'? I know a bit of group theory but cannot figure out this link. Feb 10, 2014 at 1:19
• @huotuichang The Poincare algebra has two quadratic Casimir invariant: the square of the cuadri-momentum (the particle's mass) and the square of the Pauli- Lubanski (related to the spin or helicity of the particle), which self-commute. Therefore, the eigenvalues of these operators are good label. This classification is originally due to Wigner. Elementary particles are also classified according to the way they transform under the gauge group of the standard model $U_y(1)\times SU_l(2)\times SU_c(3)$ Feb 10, 2014 at 8:58
• What's wrong with treating "elementary" particles as quasiparticles of a medium described with Poincare symmetries? Oct 23, 2015 at 5:17
• @Slaviks I'd say that you need to say (or hypothesize) what the fundamental constituents of the Poincare invariant medium are, so that you can establish a relation between the quasiparticles and the elementary degrees of freedom. There are people who think that way. Oct 23, 2015 at 15:09

In the context of condensed matter physics:

To make it short, and with the caveat that it is not a universally accepted definition, an elementary excitation may be called a quasiparticle if it is fermionic (e.g. dressed electron), and collective excitation if it is bosonic in nature (e.g. phonon, magnon).

But there is not clear cut and absolute divide between such terms, and you will not get into trouble for using them in a lax manner.

• The question asks about the difference between quasiparticles and elementary particles. Feb 6, 2014 at 22:39
• Hi drake, thank you for the comment, but I read "When is quasiparticle same as elementary excitation". Feb 7, 2014 at 8:43
• Hello, you read correctly, but excitation=particle, while elementary$\neq$collective . Thanks. Feb 7, 2014 at 17:28
• I guess we have a different understanding of the question, best would be to have huotuichang's own opinion on the interpretation of his own question, if he still cares about it a few months on. Thanks. Feb 7, 2014 at 18:48
• Hi @drake, I agree with Dominique . The term "elementary excitation" has a special meaning in condensed matter physics. Feb 7, 2014 at 19:39