Recent content by pensano

Hmm, so what would one call a G-bundle with G as fiber, with left action on G? The left action dual of a principle bundle? Thanks.

Hey, I'm a little confused on the definition of a principle bundle. The basic question: "Do elements of the structure group, G, have to act on elements of the fiber, G, from the right?" I've read a bunch of papers that seem to imply that the fiber bundle structure group elements could act...

If v_i=\frac{dx^i}{dt} has units of length over time, then the coordinates of a path on the manifold, x^i, need to have units of length, and the parameter, t, needs to have units of time. But that doesn't make sense to me, since manifold coordinates just come from charts -- maps from manifold...

Hi, maybe someone could answer this for me, or at least confirm my answer. (It's not homework.) What objects, in General Relativity, carry units? My thinking is that coordinates, x^i, on manifold patches have no units. And the parameter, t, for a path x^i(t) has no units. So velocities with...

And if \tau is the proper time along a path, doesn't |v|=1?

pervect, if the magnitude of the velocity is [|v|]=\frac{m}{s} then when you integrate to get the proper time elapsed along the path \Delta \tau = \int d\tau |v| you'll get [\Delta \tau]=m. But it should be s, so I think the maginitude of velocity needs to be unitless, yes?

So it's OK then to associate units, like seconds and meters, to the coordinates of a manifold? That won't freak out the mathematicians?

Let me clarify my question. So, say you're on a part of the manifold covered by a chart with coordinates x^i. And there's some path, x^i(\tau), through that chart, parametrized by \tau. The velocity components along the path are v^i = \frac{d x^i}{d \tau} And the magnitude of the velocity is...

So... a velocity has no units? But the maginitude of a velocity does?

In general relativity, curved spacetime is described by a manifold and a metric or frame on top of it. Can the manifold coordinates carry units of, say, meters and seconds, or do the metric components have those units?