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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.