Elementary particles such as
electrons, quarks, neutrinos, protons and neutrons
are
fermions. Photons^{4} are
examples
of bosons. Elementary particles have an intrinsic
spin or turning motion, which must be a multiple
of 1/2 due to quantum mechanics. Bosons are
particles with integer spin such as 0, 1, 2,
and so on. Fermions are particles with half-integer
spin such as 1/2, 3/2, 5/2, and so on. A particle
with spin 0 does not spin at all. Since
electrons, quarks, neutrinos, protons and
neutrons have spin 1/2, they are fermions. A
bound
state^{8}
consisting of two fermions is a boson because
the spins of the two fermions add or subtract
to give an integer spin. For example, a bound
state of two quarks has spin 1 if the two quarks
spin in the same direction. If they spin in
opposite directions, the spins subtract and
the bound state has spin 0. In either case, a
boson is obtained. In general, a bound state
of an even number of fermions is always a boson. For
example, since the helium-4 nucleus consists
of four fermions -- two protons and two
neutrons, it is a boson. In general, a bound
state of an odd number of fermions is always
a fermion. For example, since the helium-3 nucleus
consists of three fermions -- two protons
and one neutron, it is a fermion. A bound
state of any number of bosons is always a
boson because you can never add or subtract
integers to obtain a half-integer.