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Lipkin’s conservation law in vacuum electromagnetic fields

Smith, G., Strange, Paul (2018) Lipkin’s conservation law in vacuum electromagnetic fields. Journal of Physics A: Mathematical and Theoretical, 51 (43). Article Number 435204. ISSN 1751-8121. E-ISSN 1751-8121. (doi:10.1088/1751-8121/aae15f) (KAR id:69293)


Lipkin’s zilches are a set of little-known conserved quantities in classical

electromagnetic theory. Here we report a systematic calculation of the

zilches for topologically non-trivial vacuum electromagnetic fields and their

interpretation in terms of both the physical and mathematical properties of

the fields. Several families of electromagnetic fields have been explored and

examined computationally. In these cases it is found that the zilches can be

written in terms of more familiar conserved quantities: energy, momentum

and angular momentum. Furthermore we demonstrate that the zilches also

contain information about the topology of the field lines for the fields we

have examined, thus providing a previously unsuspected aspect to their

interpretation. We conjecture that these properties generalise to all integrable


Item Type: Article
DOI/Identification number: 10.1088/1751-8121/aae15f
Uncontrolled keywords: Physics of Quantum Materials, electromagnetism, Lipkin’s zilches, knotted light
Subjects: Q Science > QC Physics > QC20 Mathematical Physics
Q Science > QC Physics > QC355 Optics
Divisions: Divisions > Division of Natural Sciences > Physics and Astronomy
Depositing User: Paul Strange
Date Deposited: 27 Sep 2018 16:21 UTC
Last Modified: 09 Dec 2022 05:22 UTC
Resource URI: (The current URI for this page, for reference purposes)

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