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Cited by 133Quantum and Classical ElectrodynamicsRelativity and Gravitational TheoryOrbital Angular Momentum in Optics

An Invariance Property of the Free Electromagnetic Field

Calkin, M. G.·1965·American Journal of Physics
DOI 10.1119/1.1971089
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Abstract

In the absence of charges and currents, Maxwell's equations are invariant under the transformation E′ = E cosθ+B sinθ, B′ = −E sinθ+B cosθ. Using Noether's theorem, we show that the corresponding conserved quantity is proportional to the difference in the number of right and left circularly polarized photons in the field.

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  • Physically meaningful properties of the field should respect the Heaviside-Larmor symmetry.

    “It follows that physically meaningful properties of the fi eld should also respect this symmetry [37] and this idea has been useful in deriving forms for the spin and orbital angular momenta of the fi eld [38, 39] and for its helicity [40 -45].”

    From Optical Dirac equation (2014) · cites this paper as [41]

  • The required form of the helicity density within the optical Dirac equation is obtained by defining the helicity operator to be Σ·p/p^2, yielding the familiar expression.

    “which is the familiar expression [40 -45, 78].”

    From Optical Dirac equation (2014) · cites this paper as [41]

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Authors
Calkin, M. G.
Affiliations
Dalhousie University (CA)
Corresponding author
Calkin, M. G.
Venue
American Journal of Physics
Publisher
American Association of Physics Teachers (AAPT)
Published
1965-11-01
Volume
33
Issue
11
Pages
958-960
ISSN
  • 0002-9505 (ISSN-L)
  • 1943-2909
DOI
10.1119/1.1971089
OpenAlex
W1988416791
Cited by
133
References
0
Citations by year
2026: 6 · 2025: 1 · 2024: 14 · 2023: 4 · 2022: 5 · 2021: 10 · 2020: 13 · 2019: 14 · 2018: 13 · 2017: 9 · 2016: 6 · 2015: 5 · 2014: 9 · 2013: 11 · 2012: 3
FWCI
0.00
Type
journal article
Language
en
Open access
closed
Locations
American Journal of Physics (publishedVersion)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Orbital Angular Momentum in Optics
Keywords
free electromagnetic field, Maxwell's equations, Noether's theorem, first integrals, circular polarization

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