How big of a field is Differential Forms?

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Discussion Overview

The discussion revolves around the topic of Differential Forms, exploring its depth, resources for further study, and its relation to other fields such as differential geometry and physics, particularly in the context of General Relativity.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant expresses enthusiasm for Differential Forms and seeks advanced materials beyond introductory resources.
  • Another participant suggests that the abundance of literature is evident from the number of hits on Google Scholar.
  • Some participants argue that Differential Forms is not a standalone field but rather a subfield of Differential Geometry, referencing various books that cover the topic.
  • One participant highlights the importance of Differential Forms in understanding General Relativity.
  • A participant mentions a specific author, Henri Cartan, and recommends his book on the subject.

Areas of Agreement / Disagreement

Participants generally agree that Differential Forms is closely related to Differential Geometry, but there is no consensus on whether it constitutes a distinct field. Multiple viewpoints regarding the categorization and resources available remain present.

Contextual Notes

Some participants reference specific books and articles, indicating a variety of resources that may be useful for further exploration, but the discussion does not resolve which materials are most appropriate for advanced study.

pantheid
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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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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.
 
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"!
 
Differential forms is key in understanding and depicting General Relativity
 

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