How big of a field is Differential Forms?

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I have been reading a lot about Differential Forms lately because its so sexy. I have a pretty good grasp of how wedge product, hodge star, and differential operator "d" work, and their application to physics (it took me some time to see how d*F=J). I want to continue reading about it because I'm sure there more to it than a 30 page article and a wikipedia page, but I don't quite see where the more advanced materials are.
 

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  • #3
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It's not really a "field". There's a book called A Geometrical Approach to Differential Forms, another book by Harley Flanders, and lots of books cover that material under the heading of differential geometry or other subjects. V.I. Arnold's Mathematical Methods of classical mechanics gives one of the best descriptions I have seen.
 
  • #5
HallsofIvy
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I would say that "differential forms" is a subfield of "differential geometry". If you think "differential forms" is sexy, take a look at "differential geometry"!
 
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Differential forms is key in understanding and depicting General Relativity
 

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