Recent content by Quchen

Alright then, Electrodynamics is surely the easiest example. Take R^4 as a manifold and assign an additional degree of freedom to each point*. In the EM case, that is an element of U(1), think of some ring everywhere in spacetime. There's now a connection on this bundle, and the connection...

I guess you're asking that on a level I'm not able to answer. I'm just getting into the topic, and all I've got is half-knowledge both on the mathematical and physical side. If you're still interested ...

Sounds reasonable. Let's see how long it takes me to stumble upon that in literature.

Oh wow. Does the theorem/proof have a name or something?

So what is needed for a connection to exist? Fanciest thing I've seen so far was the curvature form on Lie-valued bundles.

That was the physicist in me saying "tensor product of the bundles" ;)

So it's basically a section in the product space of tangent- and cotangent space?

>So really you have already encountered it. Ah, it's been called the "unit tangent bundle", so yes.

It's becoming clearer and clearer. I guess it would have been more obvious if almost all fibre bundles I've encountered hadn't been vector bundles so far. Thanks to both of you.

Ah that makes sense. The vector the covariant derivative operates with respect to merely gives a direction on the manifold, whereas in the Lie derivative, the extension of the field is considered. What the metric/connection does is provide such an extension, but that extension is a property of...

Hey there, For quite some time I've been wondering now whether there's a well-understandable difference between the Lie and the covariant derivative. Although they're defined in fundamentally different ways, they're both (in a special case, at least) standing for the directional derivative of...

Sounds good, especially because I've already got his other book, the geometry of physics. I've heard that Straumann wrote an excellent book too, but I cannot find it anywhere to have a look at the contents (at least not enough to spend 80 bucks on it).

Hey there, Does anyone know a book that consequently uses coordinate-free expressions to develop general relativity? I've been looking for something for some time now, but everything I could find just briefly introduced the reader to concepts like exterior algebra, only to (almost) never use...