Classical review on Yang-Mills theory

Abstract

This paper first introduces fields, groups, symmetries and field theory in physics to give abroad understanding of the concepts behind Yang-Mills theory. Following that, this papergives the working and understanding behind the fields and transformations for the standardmodel in 3 parts, the U(1) gauge group, the SU(2) gauge group and the SU(3) gauge group. Itis shown how in U(1) due to the associated symmetry, the transformations are simpler hencethe theory is less complicated but the theories get more complicated when the symmetriesare associated with the SU(2) and SU(3) groups with more terms and more complex fieldstrength tensor. Finally, the paper ends with an explicit show of U(1) and SU(2) gauge theorywith the EM fields, current density, particle dynamics, particle charge using electrodynamicsas an example.