Quantum-mechanical description of Lense-Thirring effect for relativistic scalar particles

TL;DR

This paper provides a quantum-mechanical analysis of the Lense-Thirring effect for scalar particles using the Foldy-Wouthuysen Hamiltonian, deriving operators for angular momentum, velocity, and acceleration in Kerr spacetime.

Contribution

It introduces a quantum framework for the Lense-Thirring effect, including exact Hamiltonian expressions and operator equations in Kerr spacetime, extending classical frame-dragging concepts to quantum particles.

Findings

Derived the exact quantum evolution of angular momentum in Kerr spacetime.

Formulated quantum equations for velocity and acceleration operators.

Provided a quantum description of frame-dragging effects.

Abstract

Exact expression for the Foldy-Wouthuysen Hamiltonian of scalar particles is used for a quantum-mechanical description of the relativistic Lense-Thirring effect. The exact evolution of the angular momentum operator in the Kerr field approximated by a spatially isotropic metric is found. The quantum-mechanical description of the full Lense-Thirring effect based on the Laplace-Runge-Lenz vector is given in the nonrelativistic and weak-field approximation. Relativistic quantum-mechanical equations for the velocity and acceleration operators are obtained. The equation for the acceleration defines the Coriolis-like and centrifugal-like accelerations and presents the quantum-mechanical description of the frame-dragging effect.