2022-05-18T21:05:39Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/698592018-04-25T23:44:11Zhdl_2115_45007hdl_2115_116Spectral analysis of a massless charged scalar field with spacial cut-offWada, Kazuyuki410The quantum system of a massless charged scalar field with a self-interaction is investigated. By introducing a spacial cut-off function, the Hamiltonian of the system is realized as a linear operator on a boson Fock space. It is proven that the Hamiltonian strongly commutes with the total charge operator. This fact implies that the state space of the charged scalar field is decomposed into the infinite direct sum of fixed total charge spaces. Moreover, under certain conditions, the Hamiltonian is bounded below, self-adjoint and has a ground ground state for an arbitrarily coupling constant. A relation between the total charge of the ground state and a number operator bound is also revealed.Departmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69859info:doi/10.14943/84199https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69859/1/pre1055.pdfHokkaido University Preprint Series in Mathematics10551242014-05-08engpublisher