https://doi.org/10.1140/epjp/s13360-025-06333-w
Regular Article
Rotations and boosts of Hermite functions
1
Department of Physics, Faculty of Science, University of Zagreb, Bijenicka cesta 32, 10000, Zagreb, Croatia
2
Faculty of Mathematics, University of Rijeka, Radmile Matejcic 2, 51000, Rijeka, Croatia
3
Dipartimento di Fisica e Astronomia ‘Galileo Galilei’e INFN sez. di Padova, Universita di Padova, Via Marzolo 8, 35131, Padova, Italy
4
Faculty of Physics, University of Rijeka, Radmile Matejcic 2, 51000, Rijeka, Croatia
5
, Vienna, Austria
Received:
13
May
2024
Accepted:
15
April
2025
Published online:
28
May
2025
We provide transformation matrices for arbitrary Lorentz transformations of multi-dimensional Hermite functions in any dimension. These serve as a valuable tool for analyzing spacetime properties of MHS fields, and aid in the description of the relativistic harmonic oscillator and digital image manipulation. We also focus on finite boosts and rotations around specific axes, enabling us to identify the Lorentz Lie algebra generators. As an application and to establish a contact with the literature we construct a basis in which the two dimensional rotation operator is diagonal. We comment on the use of hypergeometric functions, the Wigner d-functions, Kravchuk polynomials, Jacobi polynomials and generalized associated Legendre functions.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
