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We slightly extend prior results about the derivation of theMaxwell-Schr\"odinger equations from the bosonic Pauli-Fierz Hamiltonian. Moreconcretely, we show that the findings from [SIAM J. Math. Anal. 52(5),4900-4936 (2020)] about the coherence of the quantized electromagnetic fieldalso hold for soft photons with small energies. This is achieved with the helpof an estimate from [arXiv:2202.05015] which proves that the domain of thenumber of photon operator is invariant during the time evolution generated bythe Pauli-Fierz Hamiltonian.

Derivation of the Maxwell-Schr\"odinger Equations: A note on the infrared sector of the radiation field