# A classification of finite quantum kinematics

@article{Tolar2014ACO, title={A classification of finite quantum kinematics}, author={J. Tolar}, journal={arXiv: Quantum Physics}, year={2014} }

Quantum mechanics in Hilbert spaces of finite dimension $N$ is reviewed from the number theoretic point of view. For composite numbers $N$ possible quantum kinematics are classified on the basis of Mackey's Imprimitivity Theorem for finite Abelian groups. This yields also a classification of finite Weyl-Heisenberg groups and the corresponding finite quantum kinematics. Simple number theory gets involved through the fundamental theorem describing all finite discrete Abelian groups of order $N… Expand

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