On what kind groups of Lie groups are Yang-Mills theories based?

Asked Mar 12 '17 at 18:34

Active Mar 12 '17 at 18:37

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According to https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_theory:

Yang–Mills theory is a gauge theory based on [...] any compact, semi-simple Lie group.

But the symmetry group of Standard Model, i.e. ${SU(3)}\times{SU(2)}\times{U(1)}$, is not semisimple, due to the $U(1)$ factor, right? What am I missing here?

edited Mar 12 '17 at 18:37

Qmechanic

201,751

asked Mar 12 '17 at 18:34

user3257624

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Essentially a duplicate of http://physics.stackexchange.com/q/52452/2451 – Qmechanic Mar 12 '17 at 18:40
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You're missing nothing, it's not semisimple, having an Abelian factor is a special case that's not included in the Wikipedia definition of a Yang-Mills theory. What is the physics question here? – ACuriousMind Mar 12 '17 at 18:40
"On what kind groups of Lie groups are Yang-Mills theories based?" – user3257624 Mar 12 '17 at 18:44

On what kind groups of Lie groups are Yang-Mills theories based?

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