Help -- Writing Lagrangian in different Representations

[Karatechop250]

Okay, so I am trying to understand on how to write Lagrangian in different representations. I know the formula of the SU(3) lagrangian in terms of the 3 and 3* rep. Now presume I have a model in the SU(3) 10 plet rep which includes exotic fermions not in the SM. How would I write out the lagrangian for this new model ? Does anyone know of any sources on writing lagrangians in different representations.

 

[Greg Bernhardt]

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

 

[samalkhaiat]

Okay, so I am trying to understand on how to write Lagrangian in different representations. I know the formula of the SU(3) lagrangian in terms of the 3 and 3* rep. Now presume I have a model in the SU(3) 10 plet rep which includes exotic fermions not in the SM. How would I write out the lagrangian for this new model ? Does anyone know of any sources on writing lagrangians in different representations.

What are these fermions?
$$\mathcal{ L } = i \bar{ [ 10 ] } \gamma^{ \mu } \partial_{ \mu } [ 10 ]$$