### 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.

Language | English |
---|---|

Article number | 123019 |

Number of pages | 27 |

Journal | New Journal of Physics |

Volume | 14 |

DOIs | |

Publication status | Published - 12 Dec 2012 |

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### Keywords

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

### Cite this

*New Journal of Physics*,

*14*, [123019]. https://doi.org/10.1088/1367-2630/14/12/123019

}

*New Journal of Physics*, vol. 14, 123019. https://doi.org/10.1088/1367-2630/14/12/123019

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Electric-magnetic symmetry and Noether's theorem

AU - Cameron, Robert P.

AU - Barnett, Stephen M.

PY - 2012/12/12

Y1 - 2012/12/12

N2 - 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.

AB - 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.

KW - electromagnetism

KW - particle physics

KW - Maxwell equations

KW - electric–magnetic symmetry

KW - Lipkin’s zilches

UR - http://www.scopus.com/inward/record.url?scp=84871914910&partnerID=8YFLogxK

U2 - 10.1088/1367-2630/14/12/123019

DO - 10.1088/1367-2630/14/12/123019

M3 - Article

VL - 14

JO - New Journal of Physics

T2 - New Journal of Physics

JF - New Journal of Physics

SN - 1367-2630

M1 - 123019

ER -