# Counting operators with group theory

1. Apr 6, 2017

### Luca_Mantani

1. The problem statement, all variables and given/known data
I have an exercise that I do not know how to solve. $N$ is a nucleon field, in the fundamental representation of $SU(4)$. We want to classify operators by their $SU(4)$ transformation properties, bearing in mind that the nucleon is a fermion and we need antisymmetric products of fields in our operators. The problem asks to combine the representations for two $N$'s and two $N^\dagger$'s and count the number of operators (with no derivatives) from counting the representations. The operator to consider is:
$$(N^\dagger N)(N^\dagger N)$$

2. Relevant equations
The problem provide these two helpful equations:
$$4\otimes \bar{4}=1\oplus 15$$
$$4\otimes 4 = 6\oplus 10$$

3. The attempt at a solution
I don't know where to start, I only know that the solution has to be of the form $x\oplus y \oplus z$. Also as a follow up question, it asks to find out if each of these representations has a $SU(2)$ singlet subgroup or not.

It would be helpful if someone know hot to tackle this kind of problem and is willing to explain to me the procedure.
Thanks in advance!

2. Apr 11, 2017

### PF_Help_Bot

Thanks for the thread! This is an automated courtesy bump. 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? The more details the better.

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