Why is it interesting?

Layman?

Why not start with quarks? Teachers investigate a learning unit on the subatomic structure of matter with 12-year-olds by Gerfried J. Wiener, Sascha M. Schmeling and Martin Hopf

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First of all, for a Lorentz-invariant theory the space of single-particle states for a given particle species must be the basis for an irreducible representation of the Lorentz group. Indeed, if the representation were reducible, there would be different states that cannot be brought into one another by any Lorentz transformation. In this case it is natural to talk of different particle species rather than of different states of the same particle. […] Massless particles have no rest-frame—thus there is no reference frame where we can apply our non-relativistic QM knowledge about rotations and spin.

http://phys.columbia.edu/~nicolis/GR_from_LI.pdf

Particles can be elementary or composite. An elementary particle cannot be decomposed into parts. We do not have an exact criterion for elementary particles. However, Wigner has proposed a necessary but not sufficient condition. A free electron should be a free electron in all relativistic frames. Any two states of a.free elementary particle should be connectible by a transformation in the Poincare group. Thus all its states are representable by superposition of states obtained by relativistic transformations of a single state. In other words,there must be no relativistically invariant subspaces for the state space of a free elementary particle, otherwise we would call the invariant subspaces elementary. The state space of a free elementary particle is the Hilbert space for an irreducible representation of the Poincare group. Wigner had worked out the irreducible representations of the Poincare group. The group-theoretic analysis shows there are two characteristics that are invariant under relativistic transformations. These characteristics are identified as the mass m and spin s. The spin is the angular momentum in the restframe, it determines the number of linearly independent states that have the same momentum four-vector. To each (m, s) there corresponds only one irre-ducible representation up to unitary equivalence. The masses of the particle can be zero or positive; the values of the finite masses are not determined byrelativistic invariance. If a particle has finite mass, then s can be 0, 5, 1, or|, . . . . If the mass is zero, the spin is either 1 or 2. Neglecting dynamical effects, the general conceptual framework for the kinematic characteristics of types of free particles can be obtained from spatio-temporal invariance. Thus pure relativistic considerations single out mass and spin as indices for the classification of various free elementary particles and put certain constraints on their values. The specific mass and spin values for a particular species of particles must be determined empirically.

From "How is Quantum Field Theory possible" by Auyang

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