Field-Strength tensor in Yang-Mills theory with Higgs field in the adjoint representation

  • #26
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Thanks. The line
note that ##[\partial_\mu, A_\nu]\Phi = \partial_\mu(A_\nu\Phi) - A_\nu \partial_\mu \Phi = (\partial_\mu A_\nu)\Phi##
contains my misunderstanding, namely, the wrong or missing parentheses in my interpretation.

I already feared you would beat me with an avalanche of indices as you said:
Sorry, I cannot answer this without writing a lot of LaTeX and I an on my phone. I might not have time to sit down by the computer until sometime Monday. Remind me if I forget.
So I'm happy that it was so easy and embarrassed that I missed the point.
 
  • #27
Orodruin
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I am happy some part of the post was useful. I spent the better part of the morning on it. :oldeyes:
 
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  • #28
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I am happy some part of the post was useful. I spent the better part of the morning on it. :oldeyes:
Well, the serious read will take some more time than to figure out my mistake.
It at least got you an additional like :wink: plus I will not complain (I already did in an insight) about
It is quite common not to write out ##\rho##, but instead just write ##A_\mu##
although I think it would generally help especially if the vectors are simultaneously matrices themselves, or if more than one representation is considered. I often wrote ##\dot{A}_\mu## on my board to save time to mark it as ##\rho(A_\mu)## but I admit that this is even more confusing in a physical context.
 
  • #29
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wow, thanks guys! This is very comprehensive and I think it really solved my problem! :smile:
 
  • #30
Orodruin
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Well, the serious read will take some more time than to figure out my mistake.
It at least got you an additional like :wink: plus I will not complain (I already did in an insight) about

although I think it would generally help especially if the vectors are simultaneously matrices themselves, or if more than one representation is considered. I often wrote ##\dot{A}_\mu## on my board to save time to mark it as ##\rho(A_\mu)## but I admit that this is even more confusing in a physical context.
It is actually very confusing in a physical context as a dot usually is taken to mean some sort of time derivative ... In general, there are so many implied indices in QFT that you would go mad if you had to write them all out...
 
  • #31
Orodruin
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Also, just a notational issue: The notation should be ##F_{\mu\nu}##, not ##F_{\mu,\nu}##. It is quite common to use ##,\mu## as additional subscripts instead of writing out ##\partial_\mu## in front.
 

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