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We show the existence of Lorentz invariant Berry phases generated, in theStueckleberg-Horwitz-Piron manifestly covariant quantum theory (SHP), by aperturbed four dimensional harmonic oscillator. These phases are associatedwith a fractional perturbation of the azimuthal symmetry of the oscillator.They are computed numerically by using time independent perturbation theory andthe definition of the Berry phase generalized to the framework of SHPrelativistic quantum theory.

Lorentz Invariant Berry Phase for a Perturbed Relativistic Four Dimensional Harmonic Oscillator