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Fundamental properties of the Hamiltonian of a Dirac particle coupled to the quantized radiation field
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 |
Publisher: | Department of Mathematics, Hokkaido University |
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
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Submitter: 数学紀要登録作業用
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