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Section 6.3 Relation between Statistics and Spin

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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, 1, 2, … 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, 3/2, 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.

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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.

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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. 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.

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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.