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Hokkaido University Preprint Series in Mathematics >
Physical subspace in a model of the quantized electromagnetic field coupled to an external field with an indefinite metric.
| Title: | Physical subspace in a model of the quantized electromagnetic field coupled to an external field with an indefinite metric. |
| Authors: | Suzuki, Akito Browse this author |
| Issue Date: | 7-Dec-2007 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 886 |
| Start Page: | 1 |
| End Page: | 26 |
| Abstract: | We 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. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69695 |
| 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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