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?

  • $\begingroup$ If I understand what you mean by "conformal connection" correctly, then no, no gauge theory may be written in terms of it because gauge theories lack the solder forms that Cartan connections come with. (That is, the principal bundle of gauge connections is not tied to the geometry of spacetime itsef as is the case with Cartan connections) $\endgroup$
    – ACuriousMind
    Apr 20, 2016 at 10:41
  • $\begingroup$ Related: physics.stackexchange.com/q/64603/2451 $\endgroup$
    – Qmechanic
    Apr 20, 2016 at 11:45
  • $\begingroup$ To reopen this post (v2) consider focusing the question. Note that res. recom. questions (i.e. a CW tagged with the res. recom. tag) usually cannot be blend with actual physics questions. (And that all questions implicitly are a request for res. recom.) $\endgroup$
    – Qmechanic
    Apr 20, 2016 at 11:50
  • $\begingroup$ If you are studying conformal structures, the physics counterpart are the conformal field theories, which can be defined on conformal manifolds (while a general QFT requires metric structure). Much of the work done in physics is for conformally flat manifolds, but there definitely are some works on curved setting as well. $\endgroup$ Apr 21, 2016 at 6:20