
#37
Jul1007, 07:43 AM

P: 344

BTW concerning the big mystery of why the physical world can be described by mathematics, that is certainly the most fundamental issue of all. And if physics is derived from logic (as Mike2 suggests, and would be great if he shows a proof that is so), one would have to end up with the same mystery: why the physical world can be described by logic. For me, the issue seems not to have progressed much and I would even say that it still revolves around a Kantian metaphysics on the basis of the human intellect. There is no obvious way to approach the question of the correspondence of the physical world (up to simplifying assumptions) to our mathematical internal formulations from a scientific point of view. There is still too much to be learned. 



#38
Jul1007, 08:41 AM

P: 344





#39
Jul1307, 12:04 PM

P: 169

First, the central charge c is an integer multiple of 24. Second, as a consequence, the partition function is really a welldefined number, not just defined up to (24/c)th root of unity. In other words, it's "modular invariant". These two are very important in Witten's paper. Third, as another consequence, the Schwinger functions, otherwise known as "npoint functions" are all welldefined meromorphic functions  that is, holomorphic except for poles. This is not so important in Witten's paper, though. nice thing is that  modulo a certain conjecture  Schellekens classified these conformal field theories for k = 1. He doesn't actually find the relevant conformal field theories with c = 24k for higher values of k. He just figures out their supposed partition functions. Since the coefficients of their partition functions are  just as in the k = 1 case  dimensions of representations of the Monster group, it seems awfully plausible that these theories (if they really exist!) have the Monster group as symmetries. However, this is something one would want to check. Nobody seems to know a c = 48 theory with Monster group symmetries, for example. I will copy your questions and my answers to the nCategory Cafe, and hope some experts on conformal field theory (like Urs Schreiber and Jacques Distler) can help us out. 



#40
Jul1307, 02:00 PM

P: 344

Dear John Baez,
Thanks a lot. I'll go in more detail into what you have written and of course I'll read with great interest your new TWF and blog entry. Over at my blog, I have linked the question of "holomorphic" factorization to the wikipedia article on the Weierstrass factorization theorem, in special, I was thinking about the section "Holomorphic functions can be factored" of that article. Please let me know whether you think that is a right pointer or not. I'll add a link to the new TWF/nCategory Café entry over at my blog opportunely. Thanks, Christine 


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