Spectrum of the semi-relativistic Pauli–Fierz model II
Takeru Hidaka
Kyushu University, Fukuoka, JapanFumio Hiroshima
Kyushu University, Fukuoka, JapanItaru Sasaki
Shinshu University, Matsumoto, Japan
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Abstract
We consider the ground state of the semi-relativistic Pauli–Fierz Hamiltonian
Here denotes the quantized radiation field with an ultraviolet cutoff function and the free field Hamiltonian with dispersion relation . The Hamiltonian describes the dynamics of a massless and semi-relativistic charged particle interacting with the quantized radiation field with an ultraviolet cutoff function. In 2016, the first two authors proved the existence of the ground state of the massive Hamiltonian is proven. Here, the massive Hamiltonian is defined by with dispersion relation . In this paper, the existence of the ground state of is proven. To this aim, we estimate a singular and non-local pull-through formula and show the equicontinuity of with some , where denotes the formal kernel of the annihilation operator. Showing the compactness of the set , the existence of the ground state of is shown.
Cite this article
Takeru Hidaka, Fumio Hiroshima, Itaru Sasaki, Spectrum of the semi-relativistic Pauli–Fierz model II. J. Spectr. Theory 11 (2021), no. 4, pp. 1779–1830
DOI 10.4171/JST/386