Foundations of Physics

, Volume 44, Issue 11, pp 1156–1167 | Cite as

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

  • Yossi Bachar
  • Rafael I. Arshansky
  • Lawrence P. Horwitz
  • Igal Aharonovich


We show the existence of Lorentz invariant Berry phases generated, in the Stueckelberg–Horwitz–Piron manifestly covariant quantum theory (SHP), by a perturbed four dimensional harmonic oscillator. These phases are associated with a fractional perturbation of the azimuthal symmetry of the oscillator. They are computed numerically by using time independent perturbation theory and the definition of the Berry phase generalized to the framework of SHP relativistic quantum theory.


Relativistic quantum mechanics Geometric phase  Stueckelberg theory Covariant 4D oscillator Induced representation 


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Yossi Bachar
    • 1
  • Rafael I. Arshansky
    • 2
  • Lawrence P. Horwitz
    • 1
    • 3
    • 4
  • Igal Aharonovich
    • 1
  1. 1.Department of PhysicsBar Ilan UniversityRamat GanIsrael
  2. 2.Givat ZorfatitJerusalemIsrael
  3. 3.School of Physics and AstronomyTel-Aviv UniversityTel AvivIsrael
  4. 4.Department of PhysicsAriel University in the ShomronArielIsrael

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