The currently accepted and experimentally welltested
theory of electromagnetic and weak interactions is called the Standard
Model. The Standard Model is based on relativistic
quantum gauge field theory. When physicists in the 1920s tried
to combine quantum mechanics of Heisenberg and Schrodinger with the
special relativity of Einstein, they unleashed a can of worms that was
only closed mathematically with the development of relativistic
quantum field theory.
The application of relativistic
quantum field theory to the classical electromagnetism of Maxwell
opened a new can of worms. The Maxwell equations possess a special local
symmetry called gauge invariance whereby
the photon field, also called the vector potential, transforms as
This transformation leaves the field strength
action
and all physical observables unchanged. In the case of electromagnetism,
the transformations that leave the action unchanged form a gauge
group known as the unitary group U(1).
An understanding of the quantum aspects of gauge invariance
led to the development of relativistic quantum
gauge field theory. Gauge invariance is a powerful symmetry that
tames uncontrollable infinities in quantum amplitudes and encodes the
rich symmetry structure of conserved charges observed in elementary
particle physics.
Today,
three of the observed forces in Nature have been successfully described
as theories of quantum gauge symmetry, and it turns out that
these three forces can be described in terms of unitary
groups of different dimensions. Physicists write this combination
of gauge groups as SU(3)xSU(2)xU(1).
In the quantum gauge theory described by the group
SU(N), there end up being N^{2}1
gauge bosons.The group SU(3) is the
gauge group of the theory of the strong interactions known as QCD.
The massless gauge field of this theory is known as the gluon. The group
SU(3) has eight generators, and this
turns out to mean that there are eight types of gluons predicted by
the theory.
The SU(2)xU(1) part
that remains is a bit more complicated. One might expect that the U(1)
refers to electromagnetism, with its single massless gauge boson, known
to everyone as the photon. So the SU(2)
must refer to the weak interaction. The group SU(2)
has three generators of gauge symmetry, and that would give three massless
gauge bosons to mediate the weak nuclear force.
But
that's wrong.
The
weak nuclear force is a short range force, behaving as if the gauge
bosons are very heavy. In order to make a gauge invariant theory work
for the weak nuclear force, theorists had to come up with a way to make
heavy gauge bosons in a way that wouldn't destroy the consistency of
the quantum theory.
The method they came up with is called spontaneous
symmetry breaking, where massless gauge bosons acquire mass by
interacting with a scalar field called the Higgs field. The resulting
theory has massive gauge bosons but still retains the nice properties
of a fully gauge invariant theory where the gauge bosons would normally
be massless.
In the end, the successful theory is called electroweak
theory, because electromagnetism and the weak nuclear force start
out being mixed together in an overall SU(2)xU(1)
gauge symmetry. The scalar field interactions mix up the four massless
gauge bosons, and out of the mixture, there winds up being three massive
gauge bosons, now called the W^{+},
W^{} and Z, and one massless gauge boson, the photon,
the carrier of the electromagnetic force. The only explicit remaining
gauge symmetry is the U(1) of electromagnetism.
Particle
physicists describe this as saying that the symmetry of SU(3)xSU(2)xU(1)
is spontaneously broken down to SU(3)xU(1)
at the electroweak scale of about 100GeV.
