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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). p. 435204. ISSN 1751-8121. E-ISSN 1751-8121. (doi:10.1088/1751-8121/aae15) (Access to this publication is currently restricted. You may be able to access a copy if URLs are provided)

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https://doi.org/10.1088/1751-8121/aae15f

Abstract

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 fields.

Item Type: Article
DOI/Identification number: 10.1088/1751-8121/aae15
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: Faculties > Sciences > School of Physical Sciences
Depositing User: Paul Strange
Date Deposited: 27 Sep 2018 16:21 UTC
Last Modified: 17 Jul 2019 10:42 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/69293 (The current URI for this page, for reference purposes)
Strange, Paul: https://orcid.org/0000-0001-5818-8032
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