$* d *$ 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