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

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.