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Rezaderex

- 5

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Im new on this forum, have been lurking around paying attention to all the interesting stuff you guys talk about, and now iv joined up!

Firstly, I am not sure if I am posting in the right place - there isn't really a distinct place for a question like this. Hopefully I am in the right place.

So basically, here is the question, recently i have been working through kaluza klein theory, more specifically the original one. i.e. S^1 compactified under the usual U(1) gauge, we gain a gauge field in which we quantise around the circle, we truncate our final action and gain a low-energy action whereby coupled EM and GR field equations come out. I do know there are issues with this truncation as, we can't really truncate massive to massless fields without actually losing massless fields.

However, I am trying to figure out what would happen in a sphere. What I am basically starting off with is some generalised arbitrary Yang-Mills theory, SU(2), and trying to unify this with gravity. However, some opinions have arisen. Essentially what i would like to do is gain coupled equations for the weak nuclear field and einstein field equations. So I am sort of trying to equate SO(3) and SU(2) (I know that is said without rigor). I have a set of killing vectors for SO(3), of which i assume make make the lie algebra, also i have the yang mills theory, i.e. a generalised non-abelian theory, i have lie algebra and the field strength for this too.

The problem is that, i have been told that it might not work, as the Ricci flatness equation will not come out. This being due to S^2 having positive curvature, whilst in the original theory we only had a S^1 which in flat... iv been told the theory works better with a torus ie. U(1)^n. The issue i have with this is that i wouldve hope to try an unite weak force and gravity, and under U(1)^n i would just be getting EM in some higher dimension.

any help would be greatly appreciated, hopefully one of you guys can tell me what's up.

cheers