Timeline for How many independent equations do Maxwell's equations represent in arbitrary dimensions?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 22, 2023 at 15:27 | vote | accept | tparker | ||
| Dec 22, 2023 at 7:30 | comment | added | Ghoster | OK, I understand now. I upvoted. | |
| Dec 22, 2023 at 7:25 | comment | added | Toyesh Jayaswal | Yes, it is a 3 form in 4 dimensions, but looking at the definition of J_a *dx_a (which generalizes), it's an n-1 form generally | |
| Dec 22, 2023 at 7:23 | comment | added | Ghoster | The second bullet point explicitly says “$J$ … is the current 3-form”. | |
| Dec 22, 2023 at 7:22 | comment | added | Toyesh Jayaswal | it's not a 3 form - the dual of a 2 form is an n-2 form, d of this is an n-1 form ("pseudo vector"), the dimension of this space is also n. Under this convention, j is generally a pseudovector, not a 3 form. | |
| Dec 22, 2023 at 7:16 | comment | added | Ghoster | I think the second equation is missing a ∗. Wikipedia leaves out the second Hodge star on the inhomogeneous equation and considers the current density to be a 3-form. So how does that approach — with two 3-form equations — give the same counting for arbitrary dimension as one 3-form and one 1-form? | |
| Dec 22, 2023 at 6:26 | history | answered | Toyesh Jayaswal | CC BY-SA 4.0 |