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Journal Article

Photon position eigenvectors, Wigner's little group, and Berry's phase


Debierre,  Vincent
Division Prof. Dr. Christoph H. Keitel, MPI for Nuclear Physics, Max Planck Society;

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Hawton, M., & Debierre, V. (2019). Photon position eigenvectors, Wigner's little group, and Berry's phase. Journal of Mathematical Physics, 60(5): 052104. doi:10.1063/1.5009073.

Cite as: https://hdl.handle.net/21.11116/0000-0005-4CBE-1
We show that the cylindrical symmetry of the eigenvectors of the photon position operator with commuting components, (x) over cap, reflects the E(2) symmetry of the photon little group. The eigenvectors of (x) over cap form a basis of localized states that have definite angular momentum, (J) over cap, parallel to their common axis of symmetry. This basis is well suited to the description of "twisted light" that has been the subject of many recent experiments and calculations. Rotation of the axis of symmetry of this basis results in the observed Berry phase displacement. We prove that {(x) over cap (1), (x) over cap (2), (J) over cap (3) is a realization of the two dimensional Euclidean e(2) algebra that effects genuine infinitesimal displacements n configuration space. Published under license by AIP Publishing.