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Generalized Heisenberg-Weyl groups and Hermite functions

Enrico Celeghini, Manuel Gadella, Mariano A. del Olmo

SciPost Phys. Proc. 14, 023 (2023) · published 23 November 2023

Proceedings event

34th International Colloquium on Group Theoretical Methods in Physics


A generalisation of Euclidean and pseudo-Euclidean groups is presented, where the Weyl-Heisenberg groups, well known in quantum mechanics, are involved. A new family of groups is obtained including all the above-mentioned groups as subgroups. Symmetries, like self-similarity and invariance with respect to the orientation of the axes, are properly included in the structure of this new family of groups. Generalized Hermite functions on multidimensional spaces, which serve as orthogonal bases of Hilbert spaces supporting unitary irreducible representations of these new groups, are introduced.

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