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Eliminating unphysical photon components from Dirac-Maxwell Hamiltonian quantized in the Lorenz gauge
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| Title: | Eliminating unphysical photon components from Dirac-Maxwell Hamiltonian quantized in the Lorenz gauge |
| Authors: | Futakuchi, Shinichiro Browse this author | | Usui, Kouta Browse this author |
| Keywords: | Quantum field theory | | Dirac-Maxwell Hamiltonian | | Indefinite metric space | | Self-adjoint operators | | Gupta-Bleuler formalism | | Lorenz gauge quantization |
| Issue Date: | 1-Feb-2017 |
| Publisher: | Elsevier |
| Journal Title: | Journal of mathematical analysis and applications |
| Volume: | 446 |
| Issue: | 1 |
| Start Page: | 1060 |
| End Page: | 1104 |
| Publisher DOI: | 10.1016/j.jmaa.2016.09.006 |
| Abstract: | We study the Dirac-Maxwell model quantized in the Lorenz gauge. In this gauge, the space of quantum mechanical state vectors inevitably adopt an indefinite metric so that the canonical commutation relation (CCR) is realized in a Lorentz covariant manner. In order to obtain a physical subspace, in which no negative norm state exists, the method first proposed by Gupta and Rimier is applied with mathematical rigor. It is proved that a suitably defined physical subspace has a positive semi definite metric, and naturally induces a physical Hilbert space with a positive definite metric. Then, the original Dime-Maxwell Hamiltonian defines an induced Hamiltonian on the physical Hilbert space which is essentially self-adjoint. (C) 2016 Elsevier Inc. All rights reserved. |
| Rights: | ©2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ | | http://creativecommons.org/licenses/by-nc-nd/4.0/ |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/71448 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 臼井 耕太
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