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October 2021 Non-relativistic Pauli–Fierz Hamiltonian for less than two photons
Dagva DAYANTSOLMON, Artbazar GALTBAYAR
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Hokkaido Math. J. 50(3): 309-326 (October 2021). DOI: 10.14492/hokmj/2019-164

Abstract

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 $R$.

Acknowledgment

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.

Citation

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Dagva DAYANTSOLMON. Artbazar GALTBAYAR. "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

Information

Received: 10 July 2019; Revised: 10 June 2020; Published: October 2021
First available in Project Euclid: 17 December 2021

Digital Object Identifier: 10.14492/hokmj/2019-164

Subjects:
Primary: 81V10
Secondary: 47A10 , 47A75 , 81T16

Keywords: dressed electron states , mass renormalization , Pauli–Fierz Hamiltonian

Rights: Copyright c 2021 Hokkaido University, Department of Mathematics

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Vol.50 • No. 3 • October 2021
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