Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Hokkaido University Preprint Series in Mathematics >
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:  1Feb1999 
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 selfadjointness 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 groundstate 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
