Yang-Mills theory

Gravity and electromagnetism are very well known forces of nature because we can observe the effects that they have our world at macroscopic length scales. However, there are also two less know fundamental interactions of nature that operate at the atomic and subatomic length scales. These are the strong (carried by gluons) and weak nuclear force (carried by W and Z bosons). The fields for these forces are called Yang-Mills fields and their mathematics were worked out in the 1950s by Chen-Ning Yang and Robert Mills. The existence of these carrier particles were confirmed in the late 1970s and early 1980s by the particle accelerator experiments in Germany and Switzerland. 

Yang-Mills theory:

Chen Ning Yang and Robert Mills, in the 1950s made a proposal that demonstrated the power of symmetry and unification. Yang, in the late 40s, had been working on a theory more general and more sophisticated than Maxwell’s theory. Yang wanted to generalize the U(1) symmetry of Maxwell, to perhaps the SU(2), or perhaps, even higher symmetries to allow for even more particles. Yang’s idea was that perhaps there could be a different rotation at each point in space. This idea was incorporated into the theory that will become known as the Yang-Mills theory or gauge theory. In fact, the details of this theory were worked out in 1954. They found that this local symmetry could be satisfied, however, it required a new particle. This would be a particle, kind of like a meson and much like the W-particle of the weak interaction. However, there was a problem with this Yang-Mills particle: it possessed too much symmetry. The Yang-Mills particle did not look like anything that was observed in nature. The W-particle has a finite mass, however, this predicted Yang-Mills particle had no mass at all. Unless these symmetries could be broken, in a way that preserved the good elements of the theory, than the Yang-Mills proposal would remain a curiosity amongst physicists. 

A theory is renormalizable if there is a way to absorb the infinities that plague it’s predictions. The general consensus at this time was that the Yang-Mills theory was nonrenormalizable. It also didn’t help that theory described only massless particles while the W-particle, indeed, has mass. 

However, Gerard ‘t Hooft, in 1971, is going to show that the Yang-Mills theory, could be broken, if employing the methods of Peter Higgs, as a renormalizable theory of weak interactions. ‘T Hooft’s discovery that gauge theories were renormalizable was a huge step for physics. In fact, this was the first successful unification of forces since the time of Maxwell. This new mathematical SU(2) x U(1) symmetry found in the Yang-Mills theory is what allowed Steven Weinberg and Abdus Salam to united electromagnetism with the weak interaction into one coherent framework.