Quasi-plane waves for spin 1 field in Lobachevsky space and a generalized helicity operator

2012/05/01 by Е. М. Ovsiyuk, Ovsiyuk, E. M., К. В. Казмерчук +1 · 1 citation
Physics and Astronomy · #35 #Black Holes and Theoretical Physics #Electromagnetic Scattering and Analysis #FOS: Physical sciences #G.1 #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1205.0150

openalex publication_date 2012/05/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Spin 1 particle is investigated in 3-dimensional curved space of constant negative curvature. An extended helicity operator is defined and the variables are separated in a tetrad-based 10-dimensional Duffin--Kemmer equation in quasi Cartesian coordinates. The problem is solved exactly in hypergeometric functions, the quantum states are determined by three quantum numbers. It is shown that Lobachevsky geometry acts effectively as a medium with simple reflecting properties. Transition to a massless case of electromagnetic field is performed.

Citations

• Spin 1 particle on 4-dimensional sphere: extended helicity operator, separation of the variables, and exact solutions
• Quasi-plane waves for a particle with spin 1/2 on the background of Lobachevsky geometry: simulating of a special medium

Cited by

• Spin 1 field in the Lobachevsky space H₃: horospherical coordinates, exact solutions

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• Nonrelativistic approximation for quasi-planes waves of a spin 1 particle in Lobachevsky space
• Quasi-plane waves for a particle with spin 1/2 on the background of Lobachevsky geometry: simulating of a special medium
• Spin 1 particle on 4-dimensional sphere: extended helicity operator, separation of the variables, and exact solutions
• Spin 1 field in the Lobachevsky space H₃: horospherical coordinates, exact solutions
• On simulating a medium with special reflecting properties by Lobachevsky geometry (One exactly solvable electromagnetic problem)