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, wherefore the concrete working assumption is not fix. Besides I have a lot of freedom in writing my thesis, why I looking for interesting fields to work.
Now, I'm interested in some physical applications. I think one of the most fields 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?