TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysProc.14.023
TI  - Generalized Heisenberg-Weyl groups and Hermite functions
PY  - 2023/11/23
UR  - https://scipost.org/SciPostPhysProc.14.023
JF  - SciPost Physics Proceedings
JA  - SciPost Phys. Proc.
VL  - 
IS  - 14
SP  - 023
A1  - Celeghini, Enrico
AU  - Gadella, Manuel
AU  - del Olmo, Mariano A.
AB  - 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.
ER  -

@Article{10.21468/SciPostPhysProc.14.023,
	title={{Generalized Heisenberg-Weyl groups and Hermite functions}},
	author={Enrico Celeghini and  Manuel Gadella and Mariano A. del Olmo},
	journal={SciPost Phys. Proc.},
	pages={023},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhysProc.14.023},
	url={https://scipost.org/10.21468/SciPostPhysProc.14.023},
}