I am looking at section 7 of the textbook mentioned in the title, and he defines the G as $$G\equiv -i\langle T \psi_a(x)\psi_b(x')\rangle$$ Then says that we can construct j from this as $$j=\pm\frac{1}{2m} \lim_{r\rightarrow r'}\lim_{t'\rightarrow t+0}(\nabla_r-\nabla_{r'})G_{aa}(x,x')$$ I do not see why this is (and why it isnt zero in the limit). j($/i\hbar)$ is $\psi\nabla\psi^\dagger-\psi^\dagger\nabla\psi$so if I take $\nabla_rG$ i have (the limit ensures that we are time ordered) $$\nabla_rG = \lim_{t'\rightarrow t+0} \frac{\hbar}{2m}\nabla_r\langle\psi(x)\psi(x')\rangle$$ My confusion is that since we have r, it will only act on $\psi$ and Iwill not recover what I expect to. IS this why the r limit must appear? And then in this case, where does the $\nabla_{r'}$ arise?
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