Gravity and Geometric Phases

TL;DR

This paper investigates how a quantum particle in a stationary spacetime, specifically around a spinning cosmic string, acquires a geometric phase related to the Aharonov-Bohm effect, highlighting the interplay between gravity and quantum phases.

Contribution

It demonstrates that a quantum particle's wave function gains a geometric phase in a spinning cosmic string spacetime, linking gravitational effects to quantum geometric phases.

Findings

Particle wave function acquires a geometric phase around a cosmic string

The phase is related to the Aharonov-Bohm effect

Quantum behavior is influenced by spacetime topology

Abstract

The behavior of a quantum test particle satisfying the Klein-Gordon equation in a certain class of 4 dimensional stationary space-times is examined. In a space-time of a spinning cosmic string, the wave function of a particle in a box is shown to acquire a geometric phase when the box is transported around a closed path surrounding the string. When interpreted as an Aharonov-Anandan geometric phase, the effect is shown to be related to the Aharonov-Bohm effect.