Dynamics, symmetries, anomaly and vortices in a rotating cosmic string background

TL;DR

This paper investigates classical and quantum dynamics of non-relativistic systems in a rotating cosmic string background, revealing hidden symmetries, anomalies, and vortex structures influenced by the conical geometry and rotation.

Contribution

It introduces a novel analysis of conformally invariant systems in rotating cosmic string spacetimes, uncovering conditions for hidden symmetries and quantum anomalies related to the conical parameter and rotation.

Findings

Hidden symmetries depend on rational values of the cone parameter α.

Quantum anomalies arise when symmetry operators are only constructible for integer α.

Vortex structures emerge in multi-particle harmonic oscillator systems with specific background parameters.

Abstract

Non-relativistic conformally invariant systems in a rotating cosmic string (conical) spacetime are analyzed at the classical and quantum levels by means of the gravitoelectromagnetic interpretation of the background. Solutions of the equations of motion are found by employing a local canonical transformation, that leads to their natural interpretation in terms of Riemann surfaces. The cone parameter $\alpha$ and the angular velocity $\Omega$ of the background determine the existence of hidden symmetries. Globally defined higher order integrals associated with perihelion of geodesic orbits appear at rational values of $\alpha$. For the harmonic oscillator system with frequency $\omega$, the integrals responsible for the trajectory closure arise only for rational values of $\alpha$ and $|\gamma|=|\Omega/\omega|$, with $|\gamma|=1$ corresponding to the Landau problem. We face a quantum anomaly problem since the hidden symmetry operators can only be constructed when $\alpha$ is integer. Such operators are non-local in the case of the free particle. For the harmonic oscillator, the symmetry generators are obtained with the help of the conformal bridge transformation. We also study a multi-particle version of the harmonic oscillator system with $|\gamma|=1$ using the mean-field theory and find that the emerging vortex structure respects a singular point of the background.