Derivation of the Maxwell–Schrödinger equations: A note on the infrared sector of the radiation field


J. Math. Phys. 64, 011901

The published version is available in open access at AIP.

arXiv 2203.16368

The preprint in pdf is available at


The bibtex entry for the article can be downloaded here.


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 Leopold and Pickl [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 Ammari et al. [arXiv:2202.05015 (2022)], which proves that the domain of the number of photon operator is invariant during the time evolution generated by the Pauli–Fierz Hamiltonian.