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

2012/05/15 by Е. М. Ovsiyuk, E. M. Ovsiyuk, Ovsiyuk, E. M.
Mathematics · Physics and Astronomy · #35 #Algebraic and Geometric Analysis #Black Holes and Theoretical Physics #FOS: Physical sciences #G.1 #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #acm:35 #math-ph #math.MP #msc:35

paper · pdf · doi:10.48550/arxiv.1205.3443

13 pages

arxiv created 2012/05/15 · openalex publication_date 2012/05/15 · arxiv updated 2012/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A complete system of solutions for a field with spin 1 in the space of constant negative curvature, Lobachevsky space H₃, has been constructed. The treatment is based on 10-dimensional Duffin-Kemmer formalism extended to curved model according to tetrad method by Tetrode-Weyl-Fock-Ivanenko, and specified in horospherical coordinates. The solving procedure substantially uses a generalized helicity operator. The Lobachevsky geometry acts along z axis as a medium with simple reflecting properties. Restriction to massless case is performed as well.

Citations

• Spin 1 particle on 4-dimensional sphere: extended helicity operator, separation of the variables, and exact solutions
• Quasi-plane waves for spin 1 field in Lobachevsky space and a generalized helicity operator

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