Spectrum of the semi-relativistic Pauli-Fierz model I

Takeru Hidaka, Fumio Hiroshima

研究成果: ジャーナルへの寄稿記事

2 引用 (Scopus)

抄録

A HVZ type theorem for the semi-relativistic Pauli-Fierz Hamiltonian,H=(p⊗1-A)2+M2⊗1+V⊗1+1⊗Hf,M≥0, in quantum electrodynamics is studied. Here H is a self-adjoint operator in Hilbert space L2(Rd)⊗F≅∫Rd⊕Fdx, A=∫Rd⊕A(x)dx is a quantized radiation field and Hf is the free field Hamiltonian defined by the second quantization of a dispersion relation ω:Rd→R. It is emphasized that massless case, M=0, is included. Let E=inf σ(H) be the bottom of the spectrum of H. Suppose that the infimum of ω is m>0. Then it is shown that σess(H)=[E+m, ∞). In particular the existence of the ground state of H can be proven.

元の言語英語
ページ(範囲)330-349
ページ数20
ジャーナルJournal of Mathematical Analysis and Applications
437
発行部数1
DOI
出版物ステータス出版済み - 5 1 2016

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Hamiltonians
Electrodynamics
Hilbert spaces
Dispersion Relation
Self-adjoint Operator
Ground state
Ground State
Mathematical operators
Quantization
Hilbert space
Radiation
Theorem
Model

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

これを引用

Spectrum of the semi-relativistic Pauli-Fierz model I. / Hidaka, Takeru; Hiroshima, Fumio.

:: Journal of Mathematical Analysis and Applications, 巻 437, 番号 1, 01.05.2016, p. 330-349.

研究成果: ジャーナルへの寄稿記事

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