3 ms·
I'm not versed at all into the Hodge star operator but it feels like Maxwell's equations expressed in both systems[1] might locate the answer. With Hodge star:
by BenoitP 3y ago
I'm not versed at all into the Hodge star operator but it feels like Maxwell's equations expressed in both systems[1] might locate the answer. With Hodge star:
dF = 0
d * F = J
Expressed in GA:
∇F = J
The eyeball-difference of which (dF = 0) would be your "how GA then blends all of this together", if I understand correctly. I'd guesstimate that dF = 0 to be akin to Gauss' law; and that maybe GA somewhat incorporates that the curl of a gradient is the zero field.
[1] https://en.wikipedia.org/wiki/Mathematical_descriptions_of_the_electromagnetic_field https://en.wikipedia.org/wiki/Mathematical_descriptions_of_t...
- nyssos 3y agoThese are not quite equivalent, since using the hodge dual explicitly incorporates the geometry of space in a way left implicit by your geometric algebra formulation. The appropriate exterior algebra analogue here is simply `F = dA`. F is the electromagnetic field tensor, d is the exterior derivative, A is the 4-potential.