- #1

Anypodetos

- 17

- 1

Why do they use ordinary partial derivatives instead of covariant ones? It's clear for the definition of F

_{μν}because here the correction terms (Christoffel symbols) cancel, but I don't see how that should work for the definition of J

^{μ}. And further down, the continuity equation is given as ##\partial_μ J^μ =0 ##. Isn't this equation coordinate system dependent? How can this be a law?

The second (possibly related) issue is their use of tensor densities for D and J. This means the time component of J has a dimension of charge per unit cube, whereas using a vector would mean charge per lengh cubed; is that right? Could that somehow fix the problem with the partial derivative? The maths is beyond me, I'm afraid.