Electric-magnetic symmetry and Noether's theorem

Robert P. Cameron, Stephen M. Barnett

Research output: Contribution to journalArticle

54 Citations (Scopus)

Abstract

In the absence of charges, Maxwell's equations are highly symmetrical. In particular, they place the electric and magnetic fields on equal footing. In light of this electric-magnetic symmetry, we introduce a variational description of the free electromagnetic field that is based upon the acknowledgement of both electric and magnetic potentials. We use our description, together with Noether's theorem, to demonstrate that electric-magnetic symmetry is, in essence, an expression of the conservation of optical helicity. The symmetry associated with the conservation of Lipkin's zilches is also identified. We conclude by considering, with care, the subtle separation of the rotation and boost angular momenta of the field into their 'spin' and 'orbital' contributions.

LanguageEnglish
Article number123019
Number of pages27
JournalNew Journal of Physics
Volume14
DOIs
Publication statusPublished - 12 Dec 2012

Fingerprint

theorems
conservation
symmetry
acceleration (physics)
Maxwell equation
electromagnetic fields
angular momentum
orbitals
electric fields
electric potential
magnetic fields

Keywords

  • electromagnetism
  • particle physics
  • Maxwell equations
  • electric–magnetic symmetry
  • Lipkin’s zilches

Cite this

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Electric-magnetic symmetry and Noether's theorem. / Cameron, Robert P.; Barnett, Stephen M.

In: New Journal of Physics, Vol. 14, 123019, 12.12.2012.

Research output: Contribution to journalArticle

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