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

摘要

Spin 1 particle is investigated in 3-dimensional curved space of constantpositive curvature. An extended helicity operator is defined and the variablesare separated in a tetrad-based 10-dimensional Duffin-Kemmer equation in quasicylindrical coordinates. The problem is solved exactly in hypergeometricfunctions, the energy spectrum determined by three discrete quantum numbers isobtained. Transition to a massless case of electromagnetic field is performed.