Is perturbation/interaction hamiltonian in interaction theory time-dependent?

Question

Reading quantum field theory text, I am confused on regard to whether perturbation (or interaction equivalently) hamiltonian added to free-field hamiltonian is time-dependent or not. In Heisenberg picture, hamiltonian is an operator, so it is obviously time-dependent, but what about in Schrodinger picture? Would hamiltonian still be time-dependent overall and thus for perturbation hamiltonian?

And by QFT, I restrict to physically relevant QFTs.

hamiltonian quantum field theory quantum mechanics time

And by QFT, I restrict to physically relevant QFTs.

Keith McClary · Answer

The confusion may be that there are two different meanings of "time dependent".

In time-dependent perturbation theory, the interaction Hamiltonian is an explicit function of time. For example, an external force is temporarily turned on.

In introductory discussions of the Heisenberg vs. Schrodinger pictures, the Hamiltonian is time independent. It is sometimes said that either the operators or states are "time dependent", but this is different from the explicit time dependence in perturbation theory.

(In some approaches to scattering theory, both types of "time dependence" are involved.)

Is perturbation/interaction hamiltonian in interaction theory time-dependent?

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