I am familiar with Yang-Mills equation of motion E.O.M. (without matter or source fields) in differential form.
D∗F=0
and Bianchi identity
DF=0
where F=dA+A∧A and D=d+[A,] as the covariant derivative version of exterior derivative d.
However, in Nakahar book Geometry, Topology and Physics, Second Edition ,
we can compare E.O.M. to his (1.269) below,
and Bianchi identity to his (1.266) below.
My question is that: Did Nakahara make any mistake? Or are his equations the rewriting of my Yang-Mills Equations above? If so, how do we convert to make the rewriting precise?
![enter image description here](https://i.stack.imgur.com/jh4Sh.png)
This post imported from StackExchange Physics at 2020-11-09 09:44 (UTC), posted by SE-user annie marie heart