Suppose we have a current $J_\mu(0)$ and some (say scalar) fields $\phi(x)\psi(x)\chi(x)$. Suppose also that we don't know the commutation relations between the current and the other fields. Isn't it true that in this case one cannot contract the scalars with external states not adjacent to them? For instance suppose we want to simplify this matrix element of time ordered operators

$$ \langle p| T\{J_\mu(0) \phi(x)\psi(x)\chi(x)\}|k\rangle = \langle p| \theta(-x_0) J_\mu(0) \phi(x)\psi(x)\chi(x)+\theta(x_0)\phi(x)\psi(x)\chi(x)J_\mu(0)|k\rangle. $$

From my understanding, the scalars in the first term can only contract with the right (ket) external state and those in the second term only with the left bra external state. Am I wrong?


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