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Kevin Driscoll

1:14 AM

Good evening folks, quick question in case anyone knows off the top of their head: does the scalar potential for electromagnetism in 6+1 dimensions still satisfy the inhomogenous wave equation of the same form as it does in 3+1 dimensions?

Brandon Enright

@KevinDriscoll I'm pretty sure nobody in chat has any background in extra-dimensional physics.

ManishEarth

@BrandonEnright nuh uh

Q: Maxwell in multiple dimensions: What happens to curl?

I read this answer a while ago, and while thinking about $\nabla$, I realized something. Since the cross product can be written as a determinant, in higher dimensions we require extra vector inputs. IIRC it's called the "wedge product" in higher dimensions. Alright, how does this work when we ge...

Brandon Enright

@ManishEarth That's news to me :-)

Kevin Driscoll

1:33 AM

@ManishEarth I saw that answer but it seemed to only talk about the fields. I'm not even sure if the scalar/vector potentials even exist in the same way. (I imagine we have to turn the vector potential into some kind of antisymmetric tensor)

ManishEarth

@KevinDriscoll I know, the answer was to tell Brandon that there are people here (not me) who are good with Maxwell's equations in higher dimensions

Kevin Driscoll

@ManishEarth Ah okay. I understand.

@BrandonEnright I don't do extra-dimensional physics either, but I'm working on a QM problem with 2 particles, so a 6D helmholtz-type PDE. I Think there may be an EM analogue in temrs of the scalar potential in frequency space, but itd have to be in 6+1 dimensions for the operators to be the same.

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