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Based on the technique of noncommutative geometry, it is shown that, by meansof the concept of the theta quantization, there is an equivalence between thenotion of the modular momentum of the Aharonov-Bohm effect and the notion of anoncommutative lattice over a circle poset.

Modular Momentum of the Aharonov-Bohm Effect on Noncommutative Lattices