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A particle-field Hamiltonian in relativistic quantum electrodynamics
| Title: | A particle-field Hamiltonian in relativistic quantum electrodynamics |
| Authors: | Arai, Asao Browse this author →KAKEN DB |
| Keywords: | quantum electrodynamics | | Dirac equation | | Hilbert spaces |
| Issue Date: | Jul-2000 |
| Publisher: | American Institute of Physics |
| Journal Title: | Journal of Mathematical Physics |
| Volume: | 30 |
| Issue: | 2 |
| Start Page: | 512 |
| End Page: | 520 |
| Publisher DOI: | 10.1063/1.533341 |
| Abstract: | 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 |
| Relation: | http://www.aip.org/ |
| Type: | article |
| URI: | http://hdl.handle.net/2115/13673 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 新井 朝雄
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