Spin 1 field in the Lobachevsky space H_{3}: horospherical coordinates, exact solutions

Abstract

A complete system of solutions for a field with spin 1 in the space of constant negative curvature, Lobachevsky space H_{3}, 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.

13 pages

References in corpus (3)

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