
#37
Nov2912, 11:43 PM

P: 571





#39
Dec1812, 07:29 AM

P: 49

I think (I don't know if it's true) that the most important skill one has to acquire in order to really understand strings is differential geometry and lie groups . Differential geometry is the basic tool to use as one deals with curved surfaces , branes and other geometric structures. Even gauge theory is best expressed using fibre bundles and connections . So you can't get far in string theory without differential geometry .What I want to know is :
Is it sufficient to understand differential geometry from a practical point of view (e.g. nakahara ) or should one learn the foundations of the subject (Which means absolute ragor) (e.g. read spivak textbooks on DG) in order to be able to apply these mathematical ideas in nonconventional and nontrivial way ? 



#40
Dec1812, 07:50 AM

Sci Advisor
P: 869

I would say that Nakahara is sometimes already to rigorous. Its treatment on Fibre Bundles and gauge theories is not really a revelation; I've never understood this fetish of some people with fibre bundles anyway.
So imho Nakahara suffices for most applications, unless you really want to do diehard math. E.g., the proof that certain string theories are anomalyfree is rather involved, and I think that only reading Nakahara doesn't give a thorough understanding. On the other hand, I'm not sure how interesting that is unless you really want to be able to do the full calculation on your own. 



#41
Dec2012, 04:33 PM

P: 55





#42
Dec2112, 02:03 AM

Sci Advisor
P: 869

That's why people buy the book of Becker^2 Schwarz. It's horrible as a pedagogic introduction, but it gives a highly compressed overview of the field in less than 1000 pages. It allows people to get the overview which is needed to start research, even though it's more of a "knowing the jargon" than "understanding what's really going on". One of the hard things about research in theoretisch physics, and string theory in particular, is that you have to find a midway between understanding and being able to contribute to the field. Most people, not being geniuses, will find the following: trying to understand too much does not allow you to contribute, and trying to dive into something very specific doesn't allow you to develop a broad overview and put your findings into the bigger picture. Which can become awkwardly exposed during questions if you give a talk :P 


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