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Fundamental properties of the Hamiltonian of a Dirac particle coupled to the quantized radiation field

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83593

Title: Fundamental properties of the Hamiltonian of a Dirac particle coupled to the quantized radiation field
Authors: Arai, A. Browse this author
Issue Date: 1-Feb-1999
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 447
Start Page: 1
End Page: 62
Abstract: We study the Hamiltonian H(V, v) 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 := [EB4L2(R3)]@ :Frad, where :Frad is the Fock space of the quantized radiation field in the Coulomb gauge, V is an external field in which the Dirac particle moves, and v is a momentum cutoff function for the interaction between the Dirac particle and the quantized radi­ation field. We first discuss the self-adjointness problem of H(V, v). Then we investigate in detail properties of H := H(O, v), the Hamiltonian in the case V = 0. In this case a unitary transform it of H has a direct integral decomposition it= f3.3 H(p)dp, where H(p) is an operator on EB4:Frad, physically the polaron Hamiltonian of the Dirac particle with total momentum p E R3We define a one parameter family {H.r(P )}TE[O,l) of deformations of H(p) such that H1 (p) = H(p). On the operator HT(p), we discuss the following aspects: (i) properties of the ground-state energy; (ii) existence of a ground state; (iii) the spectrum.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69197
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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