In first quantization, the operator $J$ assumes the form $J=\sum_{i}j(x_i)$. In Fock space, it is instead written as $J=\int dx \psi^\dagger(x)j(x)\psi(x)$, where $\psi^\dagger, \psi$ are the field operators.
Is $j(x)$ an operator in Fock space or simply a function of x?
If $j(x)=\nabla^2_x$, then does it commute with $\psi^\dagger$ and $\psi$?
