Construction of a photon position operator with commuting components from natural axioms

Michał Dobrski; Maciej Przanowski; Jaromir Tosiek; Francisco J. Turrubiates

doi:10.1103/PhysRevA.107.042208

Construction of a photon position operator with commuting components from natural axioms

Título traducido de la contribución: Construcción de un operador de posición de fotones con componentes de conmutación a partir de axiomas naturales

Michał Dobrski, Maciej Przanowski, Jaromir Tosiek, Francisco J. Turrubiates

Escuela Superior de Física y Matemáticas (ESFM)

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

2 Citas (Scopus)

Resumen

A general form of the photon position operator with commuting components fulfilling some natural axioms is obtained. This operator commutes with the photon helicity operator, is Hermitian with respect to the Białynicki-Birula scalar product, and is defined up to a unitary transformation preserving the transversality condition. It is shown that, using the procedure analogous to the one introduced by T. T. Wu and C. N. Yang for the case of the Dirac magnetic monopole, the photon position operator can be defined by a flat connection in some trivial vector bundle over R3∖{(0,0,0)}. This observation enables us to reformulate the quantum mechanics of a single photon on (R3∖{(0,0,0)})×C2.

Título traducido de la contribución	Construcción de un operador de posición de fotones con componentes de conmutación a partir de axiomas naturales
Idioma original	Inglés
Número de artículo	042208
Publicación	Physical Review A
Volumen	107
N.º	4
DOI	https://doi.org/10.1103/PhysRevA.107.042208
Estado	Publicada - abr. 2023

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abstract = "A general form of the photon position operator with commuting components fulfilling some natural axioms is obtained. This operator commutes with the photon helicity operator, is Hermitian with respect to the Bia{\l}ynicki-Birula scalar product, and is defined up to a unitary transformation preserving the transversality condition. It is shown that, using the procedure analogous to the one introduced by T. T. Wu and C. N. Yang for the case of the Dirac magnetic monopole, the photon position operator can be defined by a flat connection in some trivial vector bundle over R3∖{(0,0,0)}. This observation enables us to reformulate the quantum mechanics of a single photon on (R3∖{(0,0,0)})×C2.",

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AB - A general form of the photon position operator with commuting components fulfilling some natural axioms is obtained. This operator commutes with the photon helicity operator, is Hermitian with respect to the Białynicki-Birula scalar product, and is defined up to a unitary transformation preserving the transversality condition. It is shown that, using the procedure analogous to the one introduced by T. T. Wu and C. N. Yang for the case of the Dirac magnetic monopole, the photon position operator can be defined by a flat connection in some trivial vector bundle over R3∖{(0,0,0)}. This observation enables us to reformulate the quantum mechanics of a single photon on (R3∖{(0,0,0)})×C2.

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Construction of a photon position operator with commuting components from natural axioms

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