XXXVII Workshop on Geometric Methods in Physics | 1-7.07.2018 |

VII School on Geometry and Physics | 25-29.06.2018 |

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## Jean Pierre Gazeau## Quantum Localisation on the CircleCovariant integral quantisation using coherent states for semi-direct product groups is implemented for the motion of a particle on the circle. In this case the phase space is the cylinder, which is viewed as a left coset of the Euclidean group E(2). Coherent states issued from fiducial vectors are labelled by points in the cylinder and depend also on extra parameters. Corresponding quantisations and lower symbols of basic classical observables are implemented. The quantum localisation on the circle is examined through the properties of the angle operator yielded by this procedure, its spectrum and lower symbol, its commutator with the quantum angular momentum, and the resulting Heisenberg inequality. |

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University of Bialystok |

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