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On the photon-classical electromagnetic field relationship.

Daniela Dragoman1,2

  • 1Faculty of Physics, University of Bucharest, Bucharest, Romania.

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Summary
This summary is machine-generated.

Two methods for introducing the photon wavefunction yield different localization outcomes. One method aligns with quantum uncertainty, while the other

Keywords:
phase spacephoton wavefunctionquantum–classical correspondence

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Area of Science:

  • Quantum Physics
  • Electromagnetism

Background:

  • The wavefunction is fundamental to describing quantum particles like photons.
  • Two primary approaches exist for defining the photon wavefunction: relativistic energy-momentum and electromagnetic field theory.
  • The Riemann-Silberstein vector is a key component in the electromagnetic field approach.

Purpose of the Study:

  • To compare the equivalence and consequences of two distinct methods for introducing the free-propagating photon wavefunction.
  • To investigate the implications of each method on photon localization.
  • To determine the compatibility of these formalisms within quantum mechanics.

Main Methods:

  • Analysis of the relativistic energy-momentum relationship for photon wavefunction formulation.
  • Examination of the electromagnetic field approach, utilizing Riemann-Silberstein vectors.
  • Comparison of phase space localization and the role of canonically conjugate variables and Fourier transforms.

Main Results:

  • The relativistic energy-momentum approach allows unambiguous phase space localization consistent with the quantum uncertainty principle.
  • The electromagnetic field approach's quantum or classical treatment depends on the choice of conjugate variables and Fourier transforms.
  • Despite differences in localization consequences, both formalisms are shown to be compatible.

Conclusions:

  • The choice of formalism for the photon wavefunction impacts localization properties.
  • The relativistic approach naturally incorporates quantum uncertainty principles for localization.
  • Both introduced formalisms are reconcilable within a broader theoretical framework.