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Non-relativistic conformally invariant systems in a rotating cosmic string(conical) spacetime are analyzed at the classical and quantum levels by meansof the gravitoelectromagnetic interpretation of the background. Solutions ofthe equations of motion are found by employing a local canonicaltransformation, that leads to their natural interpretation in terms of Riemannsurfaces. The cone parameter $\alpha$ and the angular velocity $\Omega$ of thebackground determine the existence of hidden symmetries. Globally definedhigher order integrals associated with perihelion of geodesic orbits appear atrational values of $\alpha$. For the harmonic oscillator system with frequency$\omega$, the integrals responsible for the trajectory closure arise only forrational values of $\alpha$ and $|\gamma|=|\Omega/\omega|$, with $|\gamma|=1$corresponding to the Landau problem. We face a quantum anomaly problem sincethe 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 harmonicoscillator, the symmetry generators are obtained with the help of the conformalbridge transformation. We also study a multi-particle version of the harmonicoscillator system with $|\gamma|=1$ using the mean-field theory and find thatthe emerging vortex structure respects a singular point of the background.

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