11 Forces in the Standard Model and Symmetries
79
There was a suspicion that the observed universality of weak forces could
also be due to the gauge principle. But there were two fundamental differences
between the weak and the electric forces. For one thing, the weak force was
short range, and secondly, unlike electricity, weak forces changed electric
charge. We needed something a bit different from electromagnetic gauge
invariance. Luckily a generalization of Weyl’s gauge invariance principle was
given by C. N. Yang and R. L. Mills in 1954. The Yang–Mills theory in
technical “lingo” is called non-Abelian gauge symmetry. It did two things: (1)
like Weyl’s gauge invariance for electricity, the Yang–Mills theory predicted
universal strength of the forces regardless of what matter it coupled to, (2)
secondly and more importantly, it allowed for the associated spin one particles
to have electric charge, so that when coupling to matter, it could change the
electric charge of, for example, a proton and make it a neutron. This is precisely
what was required for weak forces. However, unfortunately, it predicted also
that the force must be of infinite range, like electromagnetic forces. This
is because the mediating particles (and there were more than one spin one
particle in the non-Abelian theory) have zero mass. Something still had to be
understood if the gauge principle was to dictate the weak forces.
11.1 Are the Weak Forces Also from Gauge
Symmetry Like the Electric Force?
W , Z, the mediators of weak forces, took a lot longer to make their appearance
in Fermi’s theory. The history of their origin could be traced back to 1957,
when two Rochester physicists, Robert Eugene Marshak and his graduate
student E. C. George Sudarshan, suggested that the theory of weak forces
that Fermi proposed but did not specify in detail must have the so-called
V − A form. What this means is that the Fermi theory had four fermions
joined together to form the mathematical form of weak force. But how are
they joined together? First, they must obey the theory of relativity, which allows
five possibilities for the interaction if mirror symmetry is respected, and more
possibilities if mirror symmetry is not. However, Marshak and Sudarshan,
and, Feynman and Gell-Mann, reduced these five to only one form, called
(V − A) × (V − A) form. This was a major step in moving towards the
modern theory of weak interaction. The gauge theory version, now called the
standard model, can only work for V and A type forms due to theoretical
constraints. The V − A theory put more definitiveness to Fermi’s theory and
was soon confirmed by experiments. This became the standard theory of weak
79
There was a suspicion that the observed universality of weak forces could
also be due to the gauge principle. But there were two fundamental differences
between the weak and the electric forces. For one thing, the weak force was
short range, and secondly, unlike electricity, weak forces changed electric
charge. We needed something a bit different from electromagnetic gauge
invariance. Luckily a generalization of Weyl’s gauge invariance principle was
given by C. N. Yang and R. L. Mills in 1954. The Yang–Mills theory in
technical “lingo” is called non-Abelian gauge symmetry. It did two things: (1)
like Weyl’s gauge invariance for electricity, the Yang–Mills theory predicted
universal strength of the forces regardless of what matter it coupled to, (2)
secondly and more importantly, it allowed for the associated spin one particles
to have electric charge, so that when coupling to matter, it could change the
electric charge of, for example, a proton and make it a neutron. This is precisely
what was required for weak forces. However, unfortunately, it predicted also
that the force must be of infinite range, like electromagnetic forces. This
is because the mediating particles (and there were more than one spin one
particle in the non-Abelian theory) have zero mass. Something still had to be
understood if the gauge principle was to dictate the weak forces.
11.1 Are the Weak Forces Also from Gauge
Symmetry Like the Electric Force?
W , Z, the mediators of weak forces, took a lot longer to make their appearance
in Fermi’s theory. The history of their origin could be traced back to 1957,
when two Rochester physicists, Robert Eugene Marshak and his graduate
student E. C. George Sudarshan, suggested that the theory of weak forces
that Fermi proposed but did not specify in detail must have the so-called
V − A form. What this means is that the Fermi theory had four fermions
joined together to form the mathematical form of weak force. But how are
they joined together? First, they must obey the theory of relativity, which allows
five possibilities for the interaction if mirror symmetry is respected, and more
possibilities if mirror symmetry is not. However, Marshak and Sudarshan,
and, Feynman and Gell-Mann, reduced these five to only one form, called
(V − A) × (V − A) form. This was a major step in moving towards the
modern theory of weak interaction. The gauge theory version, now called the
standard model, can only work for V and A type forms due to theoretical
constraints. The V − A theory put more definitiveness to Fermi’s theory and
was soon confirmed by experiments. This became the standard theory of weak