User:Sparkyscience/Yang-Mills theory

Yang-Mills theory or Yang-Mills-Shaw theory is a mathematical generalization of Maxwell's equations. Yang-Mills equations can be used to describe the physics of the electromagnetic, weak and strong forces and forms the mathematical foundation of the Standard Model of particle physics. Yang-Mills theory primarily deals with symmetry breaking of gauge transformations. A gauge transformation is a symmetry transformation in physics that leads leads to the conservation of some local property known as a particle or quantum number (for instance the charge, spin, baryon number, lepton number etc.). A direct consequence of gauge symmetry conservation is that the relative phases between different states are unobservable.

One of the key ideas that helped Albert Einstein develop his theory of general relativity was the idea that the field equations should be the same in every co-ordinate system, Lorentz symmetry is preserved as a local property just like the symmetry principles of quantum numbers. From a modern point of view, this too is an example of a gauge symmetry. However, it is not known whether it is possible to cast general relativity as a Yang-Mills theory, which would allow the symmetry breaking of local Lorentz invariance. It is known how how to quantize Yang-Mills theories, but not general gauge theories. This unsolved issue is considered crucial for the progression of a theory of quantum gravity and is the essence the Yang–Mills existence and mass gap problem, one of the seven Millennium Prize Problems defined by the Clay Mathematics Institute, which has offered a prize of US$1,000,000 to the one who solves it.

The first observation of a broken gauge symmetry was seen in the Wu experiment, where P-symmetry (the symmetry between left and right) was violated by the weak interaction. Today broken gauge symmetries are able to explain a wide range of diverse phenomena including the Higgs mechanism, which describes how gauge bosons get their mass, to many electromagnetic phenomena such as the Aharonov–Bohm effect, Berry phase and Zeeman effect.

History
Shortly after Albert Einstein introduced his general theory of relativity in 1915, Hermann Weyl suggested an extension where the very notion of length becomes path dependant. Weyl was able to incorporate Maxwell's electromagnetic theory into a spacetime geometry.

In 1954 Chen-Ning Yang and Robert Mills published the first gauge theory of standing consequence and independently in the same year by Ronald Shaw, who was then a student of Abdus Salam’s, though he never published it except as a PhD thesis. This occurred at about the same time that mathematicians were giving the final touches to the notion of fibre bundles. It turns out fibre bundles stand in the background of both gauge theories and general relativity.

Tsung-Dao Lee and Chen-Ning Yang proposed the idea of parity nonconservation in weak interactions. Experiments conducted in 1956 by Chien-Shiung Wu established that conservation of parity was violated (P-violation) by the weak interaction and both Lee and Yang received the 1957 Nobel Prize in physics for this result.