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A particle-field Hamiltonian in relativistic quantum electrodynamics

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タイトル: A particle-field Hamiltonian in relativistic quantum electrodynamics
著者: Arai, Asao 著作を一覧する
キーワード: quantum electrodynamics
Dirac equation
Hilbert spaces
発行日: 2000年 7月
出版者: American Institute of Physics
誌名: Journal of Mathematical Physics
巻: 30
号: 2
開始ページ: 512
終了ページ: 520
出版社 DOI: 10.1063/1.533341
抄録: We mathematically analyze a Hamiltonian Hτ(V,g) of a Dirac particle—a relativistic charged particle with spin 1/2—minimally coupled to the quantized radiation field, acting in the Hilbert space F:=[ ⊕^4^L^2(R^3)]⊗ F rad, where F rad is the Fock space of the quantized radiation field in the Coulomb gauge, V is an external potential in which the Dirac particle moves, g is a photon-momentum cutoff function in the interaction between the Dirac particle and the quantized radiation field, and τ∈R is a deformation parameter connecting the Hamiltonian with the "dipole approximation" (τ=0) and the original Hamiltonian (τ=1). We first discuss the self-adjointness problem of Htau(V,g). Then we consider Hτ:=Hτ(0,g), the Hamiltonian without the external potential. It is shown that, under a general condition on g, the closure of Hτ is unitarily equivalent to a direct integral ∫<sub>R^3</sub><sup>⊕</sup>[overline Hτ(p)]dp with a fiber Hamiltonian Hτ(p) acting in the four direct sum ⊕^4Frad of Frad, physically the polaron Hamiltonian of the Dirac particle with total momentum p∈R^3.
Rights: Copyright © 2000 American Institute of Physics
資料タイプ: article
出現コレクション:雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

提供者: 新井 朝雄


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