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)