Generalised Gell-Mann and Low theorem for explicitly time-dependent hamiltonians

Question

Is there a generalisation of the Gell-Mann and Low theorem that applies to the case of explicitly time-dependent hamiltonians? (Not on the original proof which is for $H=H_{0}+e^{-\epsilon|t|}V$, but rather for $H(t)=H_{0}+e^{-\epsilon|t|}V(t)$.)

Answer 1

If the Hamiltonian is time-dependent, then the system will not necessarily remain in the ground state, which forfeits the very statement of the Gell-Mann and Low theorem.

The standard way to bypass this problem is Keldysh formalism, where one evolves the system from $t=-\infty$ to the current moment and then back, so that averaging is still done in respect to the ground state: see this answer for references.