Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  Conformal Connections in Physics

+ 4 like - 0 dislike
607 views

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

asked Apr 20, 2016 in Theoretical Physics by richard (55 points) [ revision history ]
edited May 5, 2016 by Dilaton
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)

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

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

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar$ysi$\varnothing$sOverflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...