Spin 1 particle on 4-dimensional sphere: extended helicity operator, separation of the variables, and exact solutions

2012/03/22 by В. М. Редьков, V. M. Red'kov, Е. М. Ovsiyuk +5 · 2 citations
Mathematics · Physics and Astronomy · #Nonlinear Waves and Solitons #Numerical methods for differential equations #Quantum Mechanics and Non-Hermitian Physics #acm:35 #math-ph #math.MP #msc:35

paper · pdf · doi:10.48550/arxiv.1203.5003

21 pages

arxiv created 2012/03/22 · arxiv updated 2012/03/23

Abstract

Spin 1 particle is investigated in 3-dimensional curved space of constant positive curvature. An extended helicity operator is defined and the variables are separated in a tetrad-based 10-dimensional Duffin-Kemmer equation in quasi cylindrical coordinates. The problem is solved exactly in hypergeometric functions, the energy spectrum determined by three discrete quantum numbers is obtained. Transition to a massless case of electromagnetic field is performed.

Cited by

• Quasi-plane waves for spin 1 field in Lobachevsky space and a generalized helicity operator
• Spin 1 field in the Lobachevsky space H₃: horospherical coordinates, exact solutions

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