5.3 Bosons and Fermions

Take-home message: All particles in nature are either bosons or fermions. Their statistical properties are very different: no two fermions can be in the same state, but there is no such restriction on bosons.

Bosons are particles with integer spin:

spin 0: $\rm {}^1 H$ and $\rm {}^4 He$ in ground state, pion, Higgs boson
spin 1: $\rm {}^1 H$ and $\rm {}^4 He$ in first excited state, $\rho$ meson, photon, W and Z bosons, gluons
spin 2: $\rm {}^{16} O$ in ground state, graviton.

Fermions are particles with half-integer spin:

spin ${\textstyle \frac 1 2}$: $\rm {}^3 He$ in ground state, proton, neutron, quark, electron, neutrino
spin $\frac 3 2$: $\rm {}^5 He$ in ground state, $\Delta$ baryons (excitations of the proton and neutron)

Note that a particle is either a fermion or boson. Excitations will change the spin only by an integer amount. The basic building blocks of atoms are all fermions; composite particles (nuclei, atoms, molecules) made of an odd number of protons, neutrons and electrons are also fermions, whereas those made of an even number are bosons.

Fermions obey the Pauli exclusion principle: no more than one fermion can occupy a single quantum state. (The value of the spin quantum number $m_s$ is part of the description of the state; if that is ignored then two spin- ${\textstyle \frac 1 2}$ or four spin-$\frac 3 2$ particles can occupy the same spatial state.) This is the basis of atomic structure and the periodic table, it explains the properties of metals and of white dwarves and neutron stars.

There is no exclusion property for bosons, which are free to (indeed, other things being equal, ``prefer'' to) crowd into the same quantum state. This explains the spectrum of black-body radiation and the operation of lasers, the properties of liquid $\rm {}^4 He$ and superconductors.

References

• Mandl 9.2
• Bowley and Sánchez 10.2