# Derivation of the Maxwell-Schrödinger Equations: A note on the infrared sector of the radiation field

Marco Falconi, Nikolai Leopold

Marco Falconi, Nikolai Leopold

**30/3/22**Published in : arXiv:2203.16368

We slightly extend prior results about the derivation of the Maxwell-Schrödinger equations from the bosonic Pauli-Fierz Hamiltonian. More concretely, we show that the findings from [SIAM J. Math. Anal. 52(5), 4900-4936 (2020)] about the coherence of the quantized electromagnetic field also hold for soft photons with small energies. This is achieved with the help of an estimate from [arXiv:2202.05015] which proves that the domain of the number of photon operator is invariant during the time evolution generated by the Pauli-Fierz Hamiltonian.