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

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Abstract

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.

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Authors and Affiliations

  1. Department of Physics, Bar Ilan University, Ramat Gan, Israel

    Yossi Bachar, Lawrence P. Horwitz & Igal Aharonovich

  2. Givat Zorfatit, Etzel 12/14, 9754, Jerusalem, Israel

    Rafael I. Arshansky

  3. School of Physics and Astronomy, Tel-Aviv University, Tel Aviv, Israel

    Lawrence P. Horwitz

  4. Department of Physics, Ariel University in the Shomron, Ariel, Israel

    Lawrence P. Horwitz

Authors
  1. Yossi Bachar
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  2. Rafael I. Arshansky
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  3. Lawrence P. Horwitz
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  4. Igal Aharonovich
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Correspondence to Yossi Bachar.

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Bachar, Y., Arshansky, R.I., Horwitz, L.P. et al. Lorentz Invariant Berry Phase for a Perturbed Relativistic Four Dimensional Harmonic Oscillator. Found Phys 44, 1156–1167 (2014). https://doi.org/10.1007/s10701-014-9834-9

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  • DOI: https://doi.org/10.1007/s10701-014-9834-9

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