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Yang-Mills theory you think of as a generalisation of electromagnetism, in which the gauge group U(1) gets replaced with a more general non-abelian gauge group.

 

Renormalisation is the process in which the divergences of quantum field theory are removed.

 

A basic review of gauge theories formed part of a report I did a little while ago. It can be found here.

 

Both the questions you ask are part of a large body of knowledge. It is difficult to know how much to say.

 

Knowing some geometry and in particular vector bundles and their connections would help.

Edited by ajb
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Yang-Mills field is similar to the electromagnetic filed (there are filed tensions too) but it has more complicated (non-linear) dynamics. In electromagnetism the field depends on charges which depend on fileds (coupling fileds and charges). In Yang-Mills theory the Yang-Mills filed depends also on itself directly (together with dependence from charges).

 

Renormalizations are discarding some terms in solutions. When one solves a problem by the perturbation theory, one obtains big corrections so one cannot make calculations. Sometimes some big corrections can be groupped with the mass and charge of electron. Then the whole group is called a "renormalized parameter" and the experimental value is assigned to the whole group. It is equivalent to discarding the perturbative corrections to the experimental (original) masses and charges. Doing so one obtains small corrections and finite calculation results. The latter may be fitted to the experimental data. It "works" in QED.

Edited by Bob_for_short
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