Undergrad Quarks and isospin ladder operators

[Xico Sim]

Hi, guys.

This is actually a question about quantum mechanics, but since the context in which it appeared is particle physics, I'll post it here.
On Thompson's book (page 227, equation (9.32)), we have
$$T_+ |d\bar{u}\rangle = |u\bar{u}\rangle - |d\bar{d}\rangle$$

But I thought $T_+=T_+(1)\otimes T_+(2)$, and in that case
$$T_+ |d\bar{u}\rangle = -|u\bar{d}\rangle$$

It seems like he uses $T_+=T_+(1) + T_+(2)$, and I don't know why he does that.

 

[Xico Sim]

I wasn't thinking correctly: I now know the answer. I don't know if I should delete this thread (or even if I can delete it) or if I should answer myself, for others who may have the same question to see...

 

[mfb]

or if I should answer myself, for others who may have the same question to see...

That's the best option, you are certainly not the first or last one with that question.

 

[Xico Sim]

You're right.
Well, since $T\equiv T(1) + T(2)$ (the total angular momentum operator is the sum of the angular momentum operators of each particle), we have
$$T_+\equiv T_1+iT_2=(T_1(1)+T_1(2))+i(T_2(1)+T_2(2))=T_+(1)+T_+(2)$$