  We provide transformation matrices for arbitrary Lorentz transformations of
multidimensional 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.
