Dynamics, symmetries, anomaly and vortices in a rotating cosmic string
background
- URL: http://arxiv.org/abs/2109.05161v2
- Date: Sat, 29 Jan 2022 20:50:49 GMT
- Title: Dynamics, symmetries, anomaly and vortices in a rotating cosmic string
background
- Authors: Luis Inzunza and Mikhail S. Plyushchay
- Abstract summary: Non-relativistic conformally invariant systems in a rotating cosmic string (conical) spacetime are analyzed.
Solutions of the equations of motion are found by employing a local canonical transformation.
The cone parameter $alpha$ and the angular velocity $Omega$ of the background determine the existence of hidden symmetries.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
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