/sci/ - Science & Math

>>9816779
>I have seen people write F^2 for FmunuFmunu
Then they're wrong. F^2 is the curvature, 2-form which means you can't integrate it over the (presumably) 4D manifold M unless you take the trace over form indices. *F is the Hodge dual of F, which is a 3 form, so you can integrate F*F (which is a 4-form) over M without taking the trace. Learn differential topology before posting, retard.
>how is using that notation any worse than suppressing the Lie index?
Because it's wrong. Suppressing the Lie index is not the problem, the egregious misuse of proper mathematical notation is.
In addition, in Yang-Mills theories the gauge groups are taken to be compact and connected, but otherwise arbitrary. This means that writing in explicit Lie indices doesn't do jack shit for you since you don't even know what the basis for the Lie algebra is. Besides, in actual mathematical literature, which I'm sure you have never touched in your short undergrad life, the gauge group that the Yang-Mills theory studies is clear from context, and it is only strictly needed for physical interpretations.
>stop trying so hard
I'm trying very little, and it seems to be more than sufficient in sitting your stupid ass down and make change. Don't ever reply to me again until you've learned enough to not embarrass yourself, dumbass freshman.

>>9451127
Yeah I'm out studying Ayala's paper on the cobordism hypothesis in Starbucks so I couldn't reply for the past few hours, but I'm glad you've learned how to read in the meantime.

>>9449460
Oops it seens that you've conflated trash plebian geometry with godtier topology, anon. Rookie freshman mistake, I forgive you.