Spin 1 particle on 4-dimensional sphere: extended helicity operator,   separation of the variables, and exact solutions
  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. 
V. M. Red'kov, E. M. Ovsiyuk, V. V. Kisel
math-ph math.MP