2024-03-28T11:06:51Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/696952022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Physical subspace in a model of the quantized electromagnetic field coupled to an external field with an indefinite metric.Suzuki, Akitoopen access410We study a model of the quantized electromagnetic field interacting ith an external static source in the Feynman (Lorentz) gauge and onstruct the quantized radiation field Aμ (μ = 0, 1, 2, 3) as an operatorvalued istribution acting on the Fock space F with an indefinite metric. y using the Gupta subsidiary condition @μAμ(x)(+) = 0, one can select he physical subspace Vphys. According to the Gupta-Bleuler formalism, phys is a non-negative subspace so that elements of Vphys, called physical tates, can be probabilistically interpretable. Indeed, assuming that the xternal source is infrared regular, i.e., ˆ /|k|3/2 2 L2(R3), we can characterize he physical subspace Vphys and show that Vphys is non-negative. n addition, we find that the Hamiltonian of the model is reduced to the amiltonian of the transversal photons with the Coulomb interaction. We owever prove that the physical subspace is trivial, i.e., Vphys = 0, if and nly if the external source is infrared singular, i.e., ˆ /|k|3/2 62 L2(R3). e also discuss a representation different from the above representation uch that the physical subspace is not trivial under the infrared singular ondition.Department of Mathematics, Hokkaido University2007-12-07engdepartmental bulletin paperVoRhttps://doi.org/10.14943/84036http://hdl.handle.net/2115/6969510.14943/84036Hokkaido University Preprint Series in Mathematics886126https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69695/1/pre886.pdfapplication/pdf368.21 KB2007-12-07