$* d * $ operator --- Digest the (differential/geometry) meaning

Question

I like to digest better:

• the $* d * $ operator in Maxwell differential form equation

• the $* D * $ operator in Yang-Mills differential form equation

We already knew that in Maxwell differential form equation we have: $$ * d * F=0 $$ knew that in Yang-Mills differential form equation we have: $$ * D * F=0 $$ here $D .=d .+ [A,.]$

But how we do understand $* d * $ operator and $* D * $ operator? Their the (differential/geometry) meaning? How do we make ourselves comfortable , even though we also knew the equation boils down to:

$$ \partial_\mu F^{\mu \nu}=0 $$ $$ D_\mu F^{\mu \nu}=0 $$ respectively. But how to think $* d * $ operator and $* D * $ operator differential/geometry-ly?

This post imported from StackExchange Physics at 2020-11-09 19:28 (UTC), posted by SE-user annie marie heart

Comments

Well, do you understand what $\ast$ and $d$ individually mean?

This post imported from StackExchange Physics at 2020-11-09 19:28 (UTC), posted by SE-user d_b