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

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

doi:10.1007/s10701-014-9834-9

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

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

Department of Physics - at Bar-Ilan University

Givat Zorfatit
Tel Aviv University
Ariel University

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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.

Original language	English
Pages (from-to)	1156-1167
Number of pages	12
Journal	Foundations of Physics
Volume	44
Issue number	11
DOIs	https://doi.org/10.1007/s10701-014-9834-9
State	Published - Nov 2014

Bibliographical note

Publisher Copyright:
© 2014, Springer Science+Business Media New York.

Keywords

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

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10.1007/s10701-014-9834-9

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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.",

keywords = "Covariant 4D oscillator, Geometric phase, Induced representation, Relativistic quantum mechanics, Stueckelberg theory",

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AU - Horwitz, Lawrence P.

AU - Aharonovich, Igal

PY - 2014/11

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N2 - 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.

AB - 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.

KW - Covariant 4D oscillator

KW - Geometric phase

KW - Induced representation

KW - Relativistic quantum mechanics

KW - Stueckelberg theory

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IS - 11

ER -

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

Abstract

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Keywords

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