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

TL;DR

This paper solves the quantum behavior of a spin 1 particle in Lobachevsky space using an extended helicity operator, revealing how negative curvature influences particle states and transitions to electromagnetic fields.

Contribution

It introduces an extended helicity operator and provides exact solutions for spin 1 particles in hyperbolic space, extending understanding of quantum fields in curved geometries.

Findings

Exact solutions in hypergeometric functions for spin 1 particles

Lobachevsky space acts as a reflecting medium

Transition from massive to massless electromagnetic field

Abstract

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.