# Spectrum of the semi-relativistic Pauli-Fierz model II

## 抄録

We consider the ground state of the semi-relativistic Pauli-Fierz Hamiltonian (equation presented) Here A.x/ denotes the quantized radiation field with an ultraviolet cutoff function and Hf the free field Hamiltonian with dispersion relation jkj. The Hamiltonian H 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 m of the massive Hamiltonian Hm is proven. Here, the massive Hamiltonian Hm is defined by H with dispersion relation pk2 C m2 (m > 0). In this paper, the existence of the ground state of H is proven. To this aim, we estimate a singular and non-local pull-through formula and show the equicontinuity of {a(k)φm}0<m<m0 with somem0, where a(k) denotes the formal kernel of the annihilation operator. Showing the compactness of the set m0<m<m0 , the existence of the ground state of H is shown.

本文言語 英語 1779-1830 52 Journal of Spectral Theory 11 4 https://doi.org/10.4171/JST/386 出版済み - 2021

## !!!All Science Journal Classification (ASJC) codes

• 統計物理学および非線形物理学
• 数理物理学
• 幾何学とトポロジー

## フィンガープリント

「Spectrum of the semi-relativistic Pauli-Fierz model II」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。