We consider the Pauli–Fierz model, which describes a particle (an electron) coupled to the quantized electromagnetic field and limit the number of photons to less than 2. By computing the resolvent explicitly, we located the spectrum of the Hamiltonian mass. Our results do not depend on the coupling constant $e$ nor on the infrared cutoff parameter $R$.
The authors express their gratitude to the reviewers for helpful comments and valuable suggestions that greatly improved the manuscript. This work was supported by research Grant No.12 of the Higher Education Reform Project, Mongolia and project P2020-3984, funded by the National University of Mongolia.
"Non-relativistic Pauli–Fierz Hamiltonian for less than two photons." Hokkaido Math. J. 50 (3) 309 - 326, October 2021. https://doi.org/10.14492/hokmj/2019-164