Section 6.3 Relation between Statistics and Spin
All fundamental particles are either fermions or bosons. Strangely enough, which category they fall into is directly determined by their value of spin.
All particles with spin \(s=0\text{,}\) \(1\text{,}\) \(2\text{,}\) … or integer spin, are bosons: their two-particle states must be symmetric. This includes the photon and some more exotic particles that we will encounter in Unit 4.
All particles with spin \(s=1/2\text{,}\) \(3/2\text{,}\) etc, which we call half-integer spin, are fermions: their two-particle states must be antisymmetric. These include electrons, protons, neutrons, and quarks, and more.
The connection between the spin of a particle and its symmetry under exchange (swap) does not have a simple origin, and we will not try to explain it here. But it is another rule strictly obeyed by every particle.
Note that in some cases a collection of particles can act as a single particle. For example, a proton is really made up of three quarks. Each quark is a fermion, so if we imagine exchanging a pair of protons, we are really exchanging three pairs of quarks. Each quark exchange brings in a minus sign, so the net effect of exchanging the protons in a two-proton state is a factor of \((-1)^3=-1\text{.}\) Thus, the proton will act like a fermion, as long as it makes sense to think of the proton as a unit, that is, as long as we are not considering some process that rips apart the protons.
A similar game can be played with entire atoms. A helium-4 atom consists of two protons and two neutrons in the nucleus, orbited by two electrons. That is an even number of fermions, so if we make a two-atom state out of two helium atoms, they will be symmetric under exchange of the atoms. So the helium-4 atom, if it stays intact, acts as a boson.