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Re: 4 large dimensionsPosted by phobos on July 21, 19101 at 10:07:25: In Reply to: Re: 4 large dimensions posted by Cooper on July 21, 19101 at 08:44:30: Well, there are many examples, so I don't know of any place in the literature where they would all be collected. The math stuff is somewhat pithy, but the physics is less so. For instance, one can determine whether a topological manifold can be smoothed (calculus could then be done on it) in dimensions 2 and >=5. There has been some progress in 3, but 4 remains a puzzle. The basic reason is that 2-manifolds have been completely classified (compact, orientable, closed manifolds, that is), while sufficiently large numbers of dimensions give one enough room to deform smoothly that topology becomes simpler. As for YM, it's nonrenormalizable in d>4 and instantons have singularities at small size. YM in d=2 was solved exactly by 't Hoof, and d=3 YM is pretty well understood (much like gravity in d=2,3 has been solved exactly). Thinks like confinement and a mass gap, the interesting infared physics, happen in d=4. phobos
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