QED:WeakForce:QCDU(1):SU(2):SU(3)T^1:T^2:T^3 ?

[Spinnor]

If in some theories I can think of electric charge as being quantized momentum around a circle could I think of Weak Charge as quantized momentum in the space T^2, a two-torus, or think of QCD's color charge as quantized momentum in the space T^3, a three torus? Certain directions in T^2 and T^3 might be forbidden? Whether wrong or right I'm just curious what is the natural continuation of thought on this matter is.

Thanks for any help!

 

[TriTertButoxy]

I believe you are on the right track. What you want to say is that the various charges you mentioned may be associated with what you call 'quantized momentum' in their respective group manifold. The group manifold of U(1) is isomorphic to a circle, so that's ok. But I don't know how to visualize the group manifold of SU(2), which is a three-dimensional space, and SU(3), which is an eight-dimensional space.