Recent content by LearningDG

Thanks a lot Lavinia. So correct me if I am wrong: For the same manifold, if I have two different atlas, say one is Cn and another is Cm for general m,n, which are not compatible, then I can say these are two different differential structures. Then the fact that for a manifold with dimension<4...

The reason is that a photon in a superposition of (|E1>+|E2>)/sqrt(2) is not the same as a photon with energy (E1+E2)/2.

Hi, Can anyone explain why in field theory we require [f*(x),f(y)] = 0 for space-lkie intervals x,y; but not <0|f*(x)f(y)|0> = 0? Thanks!

Thanks micromass! Yes, they determine the same topological manifold. What I am not sure is if I have constructed two maximal altas of it which are not compatible (say, one is C1 and the other is smooth), can I say these are two differential structures? If yes, I guess mathematicians have proved...

Thanks Micromass! But I still got some questions. That's exactly what I mean by two structures, viz., not smooth in one altas but smooth in the other. Or, should the transition map at least be C1? Then may be put this way, change my representation to a function which is smooth everywhere but...

Hi, I just started learning differential geometry. Got some questions. Thanks in advance to anyone who can help! Consider the one-dimensional manifold represented by the line y = x for x<0 and y = 2x for x>= 0. Now if I consider the altas with two charts p(x, y)=x for x<-1 and q(x,y)=y for...