Talk:Vierbein

Forgive me if I'm wrong here. The principal bundle (I've called it B): this is supposed given first and V constructed from it ... ? Well, I guess B and V exist in a state of mutual implication here. And the invertible vector bundle map from TM to V? That's just an isomorphism of vector bundles?

So this is all a way of saying that TM can be reduced to structure group SO(p,q), and B is the associated principal bundle? Well, if so I can read on further ...

Charles Matthews 21:13, 8 Nov 2003 (UTC)

Well, B is supposed to be deduced from V via the pullback of the connection A over V to B. Yes, e is an isomorphism between TM and V, but the catch is the structure group SO(p,q) only acts nontrivially upon V, not TM. In other words, SO(p,q) acts upon BOTH V and e in such a way that if X is any element of TM, then an element of SO(p,q), g, maps X to itself, but acts upon e in such a way as to satisfy g(e)(X)=g(e(X)). Phys 21:53, 8 Nov 2003 (UTC)

Sorry, don't understand the first sentence of that. There is no mention of A at all in the definitions, where B is introduced.

By the way, I think orthonormal frame is a more elementary notion, and redirecting to this page will make access harder for almost everyone.

Charles Matthews 13:57, 11 Nov 2003 (UTC)

OK, a reference for what is this (I take it) is Dieudonne's Treatise On Analysis, Volume IV, Chapter 20 in exercises to section 5 (section 6 being on moving frames). So, shall I try to reconstruct this along those lines?

Charles Matthews 15:44, 11 Nov 2003 (UTC)


 * I've never read that book. So I can't really say. It's up to you, I guess. Phys 15:53, 11 Nov 2003 (UTC)

An alternative is if I create a Cartan connection article separately out of that source; and that in the end vierbein and Cartan formalism get redirected there (provided it's all obviously compatible).

Charles Matthews 15:58, 11 Nov 2003 (UTC)


 * That would be fine. We probably need an article about frames in the component notation as well, because some people, especially physicists prefer the component notation. Phys 16:01, 11 Nov 2003 (UTC)