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Gauge and unitary transformations in multipolar quantum optics.

Mohamed Babiker1

  • 1School of Physics, Engineering and Technology, University of York, England, YO10 5DD, UK.

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Summary

This study introduces transformations for multipolar quantum optics, unifying gauge and unitary methods into the Power-Zienau-Woolley formulation. It reveals insights into the Röntgen and Aharonov-Casher effects in quantum electrodynamics.

Keywords:
PZW TheoryQEDQuantum Opticsmultipolar quantum optics

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Area of Science:

  • Quantum optics
  • Quantum electrodynamics
  • Atomic and molecular physics

Background:

  • Multipolar quantum optics examines light-matter interactions in many-body systems.
  • Conventional formalisms require transformation for comprehensive analysis.

Purpose of the Study:

  • To describe transformations unifying gauge and unitary approaches.
  • To derive the Power-Zienau-Woolley formulation from a non-relativistic formalism.
  • To identify Röntgen and Aharonov-Casher effects within this framework.

Main Methods:

  • Gauge transformation applied to electromagnetic fields at the Lagrangian stage.
  • Unitary transformation applied to the Hamiltonian.
  • Analysis of resulting quantum electrodynamics formulation.

Main Results:

  • The two transformations yield the Power-Zienau-Woolley formulation.
  • The formalism accounts for internal and center-of-mass motion.
  • Identification of the Röntgen and Aharonov-Casher effects.

Conclusions:

  • The multipolar formalism is a robust platform for optical processes.
  • The study clarifies the origins of the Röntgen and Aharonov-Casher effects.
  • These effects have significant theoretical and experimental implications.