Nonrelativistic approximation for quasi-planes waves of a spin 1 particle in Lobachevsky space

TL;DR

This paper derives a nonrelativistic approximation for spin 1 particles in Lobachevsky space, solving the resulting equations exactly using Bessel functions and identifying quantum states via four quantum numbers.

Contribution

It introduces a nonrelativistic approximation method for spin 1 particles in curved Lobachevsky space, utilizing a generalized helicity operator and exact solutions with Bessel functions.

Findings

Exact solutions in terms of Bessel functions for the system of equations.

Quantum states characterized by four quantum numbers.

Application of a generalized helicity operator in curved space.

Abstract

Spin 1 particle in Pauli approximation is investigated on the background of the curved space of constant negative curvature, Lobachevsky space. Nonrelativistic approximation is performed in the system of 10 equations resulted from separating the variables in Duffin-Kemmer equation specified in quasi-cartesian coordinates. The problem is solved exactly in Bessel functions, the quantum states are determined by four quantum numbers. The treatment is substantially based on the use of a generalized helicity operator in Lobachevsky space model.