Jérôme Beau

Semiclassical Consistency of the Weil Representation on Heis3(Z/qZ): Quantitative Sinc Embedding, Generator Convergence, and Aliasing Control

We prove that the rescaled Weil generators ${\hat{X}_q}$ and ${\hat{P}_q}$ of the discrete Heisenberg group ${\mathrm{Heis}_3}({\mathbb{Z}/q\mathbb{Z}})$ converge strongly to the position operator $x$ and the momentum operator $-i\partial_x$ as $q \to \infty$, in the sense of Hyp...