Using simple group theoretical arguments we show how introducing a cur
vature parameter kappa=omega/c for a harmonic oscillator of mass m and
frequency omega leads to an elementary entity of energy E0=mc2+1/2hom
egaBAR+O(kappa). This entity is a deformation of both an elementary vi
bration (rest energy 1/2homegaBAR) and an elementary particle (rest en
ergy mc2).