Methodological notes

Quantum description of a field in macroscopic electrodynamics and photon properties in transparent media

Peter the Great Saint-Petersburg Polytechnic University, ul. Polytechnicheskaya 29, St. Petersburg, 195251, Russian Federation

Applying a quantum-mechanical treatment to a high-frequency macroscopic electromagnetic field and radiative phenomena in a medium, we construct quantum operators for energy—momentum tensor components in dispersive media and find their eigenvalues, which are different in the Minkowski and Abraham representations. It is shown that the photon momentum in a medium resulting from the quantization of the vector potential differs from that defined from Abraham's symmetric energy-momentum tensor but is equal to the momentum defined from the Minkowski tensor. A similar result is obtained by calculating the intrinsic angular moment (spin) of an electromagnetic field in the medium. Only the Minkowski tensor enables experimentally confirmed multiple-of-ħ spin values, providing the grounds for choosing the Minkowski representation as the adequate form for the momentum density of a transverse electromagnetic field in a transparent medium, whether the field is treated classically or quantum mechanically. The Abraham representation is unsuitable for this purpose and leads to contradictions. The conclusion drawn does not apply to quasi-static and static fields.

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Keywords: the Minkowski energy—momentum tensor, quantum theory, radiation phenomena, spin and mass of a photon in matter
PACS: 12.20.−m, 41.20.Jb, 41.60.Bq (all)
DOI: 10.3367/UFNe.2017.04.038138
Citation: Toptygin I N "Quantum description of a field in macroscopic electrodynamics and photon properties in transparent media" Phys. Usp. 60 935–947 (2017)
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Received: 21st, June 2016, revised: 8th, April 2017, 12th, April 2017

Оригинал: Топтыгин И Н «Квантовое описание поля в макроскопической электродинамике и свойства фотонов в прозрачных средах» УФН 187 1007–1020 (2017); DOI: 10.3367/UFNr.2017.04.038138

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