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

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.

arXiv comment39 pages

References in corpus (28)

• Rapidly Rotating Atomic Gases
• Natural Wormholes as Gravitational Lenses
• SUSY in the sky
• Black holes, hidden symmetries, and complete integrability
• Gravitoelectromagnetism: A Brief Review
• Landau Levels in the Presence of Topological Defects
• `Hidden' Symmetries of Higher Dimensional Rotating Black Holes
• Higher-Dimensional Black Holes: Hidden Symmetries and Separation of Variables
• Anyon wave equations and the noncommutative plane
• Hidden Symmetries of Dynamics in Classical and Quantum Physics
• Anyon spin and the exotic central extension of the planar Galilei group
• Quantum Mechanics of Yano tensors: Dirac equation in curved spacetime
• Non-relativistic anyons, exotic Galilean symmetry and noncommutative plane
• Landau Quantization in the Spinning Cosmic String Spacetime
• Near-horizon aspects of acceleration radiation by free fall of an atom into a black hole
• Coulomb and quantum oscillator problems in conical spaces with arbitrary dimensions
• Collimated Escaping Vortical Polar e-e+ Jets Intrinsically Produced by Rotating Black Holes and Penrose Processes
• Conformal bridge between asymptotic freedom and confinement
• Inertial-Hall effect: the influence of rotation on the Hall conductivity
• ABC of ladder operators for rationally extended quantum harmonic oscillator systems
• Spinning cosmic strings: a general class of solutions
• Rational deformations of conformal mechanics
• Geometry of Lax pairs: particle motion and Killing-Yano tensors
• Conformal generation of an exotic rotationally invariant harmonic oscillator
• Conformal bridge transformation and PT symmetry
• The Cosmological Spinor
• Superconformal mechanics of AdS${}_2$ D-brane boundstates
• Overspinning naked singularities in AdS${}_3$ spacetime

Cited by in corpus (7)

• Schrödinger symmetry: a historical review
• Gravitational Waves and Conformal Time Transformations
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• Weak-strong duality of the non-commutative Landau problem induced by a two-vortex permutation, and conformal bridge transformation
• Projective Time, Cayley Transformations and the Schwarzian Geometry of the Free Particle--Oscillator Correspondence
• Conformal bridge transformation, $\mathcal{P}\mathcal{T}$- and super- symmetry