The Quanta Magazine article titled What is a Particle? has a nice summary of various possible interpretations of particles in theoretical physics, but it appears that there is no universally accepted definition as of now. Let us consider two such description:
- Group theoretic definition of particle:
Following is an excerpt from this article:
Ever since the fundamental paper of Wigner [W39] on the irreducible representations of the Poincare group, it has been a (perhaps implicit) definition in physics that an elementary particle "is" an irreducible representation of the group, $G $, of "symmetries of nature". The search for the elements then has three components:
- Determine the group $G$ (a problem in physics).
- Find the irreducible representations of G (a problem in mathematics).
- Determine which irreducible representations of $G$ occur as elementary particles. (a problem in physics).
- Particle interpretation in QFT:
Although fields are more fundamental, a particle like interpretation can emerge if we look at the interaction b/w quantum field and detector. We can start with a two level quantum system coupled to the field. The field state $|\psi\rangle$ with occupation number $n$ can exchange quanta of energy with the detector and can transition to occupation number $n+1$ or $n-1$ with some non-zero probability. Wald argues that $n$ can be interpreted as no. of particles and that this interpretation works even in curved space-time (See $\S$3.3 of "Quantum field theory in curved spacetime and black hole thermodynamics" by R.M.Wald).
While Wald's argument makes sense intuitively, is it possible to assign a group theoretic description to this process? In other words, does the exchanged quanta b/w the quantum field and the detector can be expressed as an "irreducible representation of some symmetry group"?
In general, all interactions in QFT can be described by processes involving exchange of virtual particles. While the ingoing and outgoing states can be given a group theoretic description, is it also true for virtual particles?