For my diploma thesis in Mathematics I investigate conformal connections (as an example of Cartan connections). All in all the thesis should deal with geometric aspects (associated bundles, (pseudo)-Riemannian manifolds, G-structures,...).

I just started my thoughts, where the concrete working assumption is not yet fixed. Besides I have a lot of freedom in writing my thesis; this is why I am looking for interesting fields to work.

Now, I'm interested in some physical applications. I think one of the fields most using this geometric object is general relativity. Is there a good reference (text book or paper)? Are there good references for applications in other fields, i.e. QFT?

Further I'm interested in the following question: Are there any attempts to write the Yang-Mills equations in terms of conformal connections? If not: Is it ever useful to write down the YM equations in this language?

This post imported from StackExchange Physics at 2016-05-05 11:28 (UTC), posted by SE-user Richard