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

TL;DR

This paper constructs a complete set of solutions for a spin 1 field in Lobachevsky space using an extended Duffin-Kemmer formalism in horospherical coordinates, highlighting the role of geometry and helicity.

Contribution

It introduces a novel method to solve the spin 1 field equations in curved Lobachevsky space using an extended formalism and generalized helicity operator.

Findings

Complete solutions for spin 1 fields in H_{3} are derived.

The formalism is extended to curved space using tetrad methods.

Massless case solutions are also obtained.

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.