Why? Isn't he human? :D
Anyway, relation above hasn't free indices:
g^{\mu\nu}g_{\mu\nu}
so it has to a scalar. Indeed it is dimension of manifold.
Sorry for my poor english :D
This relation is wrong.
g^{\mu\nu} g_{\mu\rho} = \delta^\nu_\rho
then, if we take \nu = \rho we obtain:
g^{\mu\nu} g_{\mu\nu} = \delta^\nu_\nu
but the last term is the trace of Kronecker delta which is four if dim(M) = 4
Locally it seems a 1-form and since there is a one to one correspondence between 1-form and vector field so potential can be viewed as vector field.
But if we take a gauge transformation we discover that it transforms as a principal connection on a principal bundle...
For Maxwell theory...
Curvature form with respect to principal connection
Hi all,
I have a question. Let us suppose that P is a principal bundle with G standard group, \omega a principal connection (as a split of tangent space in direct sum of vertical and horizontal vectors, at every point in a differential way)...