Recent content by analmux

Question: What's so extremely difficult about the mathematics used in superstring theory? I think saying an object is dimensionless differs from saying it can be regarded as dimensionless. Question: What's so philosophical about realizing that this physical extension must be...

I did some graduate student research on superstring theory, but I lost my enthousiasm for doing any more research in this topic totally. I also do mathematics, but a lot of mathematics, used in many of the articles I had to study, isn't always used in a clear way. It took ages to realize it's...

Well, you didn't ask to show it. I wrote: "The 3-sphere (S^3) can be considered as a 'manifold' isomorphic to SU(2) and the real projective space of dimension 3, which is a quotient of S^3 under 'antipodal identification' is isomorphic to SO(3). Both are orientable manifolds." Working out...

Yes, SO(3) can be interpreted as a quotient group of SU(2). {I,-I} is an abelian subgroup and it is a normal subgroup of SU(2). A quotient group G/H is always trivially related to a group G and a normal subgroup H of G. Thus, indeed SO(3) equals (or is at least isomorphic to) SU(2) after...

Just to stir up the haziness a bit...if a set can be described as a HOLOMORPHIC curve, then it IS 2-dimensional.

Well, the Ricci curvature tensor R is symmetric and it is an object with 2 lower indices, but these indices are used to represent R with respect to a coordinate. As it has two lower indices it is cotensor of rank 2, so we need to feed it with 2 vectors. We can represent R without coordinates...