2022-05-18T23:39:55Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/691972018-04-25T23:44:07Zhdl_2115_45007hdl_2115_116Fundamental properties of the Hamiltonian of a Dirac particle coupled to the quantized radiation fieldArai, A.410We 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 radiĀation 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.Departmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69197info:doi/10.14943/83593https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69197/1/pre447.pdfHokkaido University Preprint Series in Mathematics4471621999-02-01engpublisher