# How do people historically have come to use the Yang-Mills theory in physics?

There are many books, in which Yang-Mills theory is introduced "just like that". But I didn't find some book with set of historical arguments, which had led people to using it in quantum field theory. Can you tell me about this?

Maybe, my question leads to the next question: how did people guess that they need to expand the group of local gauge invariance for describing, for example, quarks?

I believe the milestone about the introduction of Yang-Mills theory from gauge invariance is the 1973 article by Ernest Abers and Benjamin Lee. You can easily find the original article on the web through a simple google search. This is a fundamental article I would recommend to everybody interested in Quantum Field Theory.

Also, I remember I found good historical, as well as logical, introductions to Y-M theory in the book by Aitchinson and Hey, and in the older one by Cheng and Li of the 1983. These are certainly good references for the history of the development of gauge theories.

Another milestone is the 1980 article by Gerardus 't Hooft, which I think could provide a great answer to your second question.

Yang-Mills theory is used in two parts of the standard model, The electroweak interactions and strong interactions (QCD).

For the history of Yang-Mills itself see https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_theory#History_and_theoretical_description

For the Electroweak theory see the histroy of the Higgs Boson https://en.wikipedia.org/wiki/Higgs_boson#History

For the history of how QCD became the theory of the strong force and quarks see https://en.wikipedia.org/wiki/Quantum_chromodynamics#History

If you want still more details see Wikipedia pages of the individuals involved or find one of the many popular books written on the history of the standard model of particle physics.

• The first part is irrelevant, and the rest are just links. $\therefore$, this is not an answer, and I'm flagging it as such. – Abhimanyu Pallavi Sudhir Sep 15 '13 at 11:40
• The question is very broad. A full self-contained answer would have to be very long if it is sure to cover what the OP's is looking for. Providing links is therefore the best way to answer the question. If you think otherwise I would like to see your answer. – Philip Gibbs - inactive Sep 15 '13 at 11:51
• I meant; that you could at least quote the content from the wp pages you've linked. WP pages may often get changed radically, or the page deleted (which happens a lot to physics articles...), rendering this answer useless. – Abhimanyu Pallavi Sudhir Sep 15 '13 at 11:54
• The wikipedia articles themselves have more links that provide useful supplementary information so if I copied them where would it end? I know the articles could change but if anything they will be improved and if they are moved it will not be hard to find what replaces them. The history of Yang Mills and the standard model is very long and it is not clear which parts resolve the question. I think links are the best way to answer it but you are free to give your own answer if you have a better idea. – Philip Gibbs - inactive Sep 15 '13 at 12:08