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Research Article | Open Access

Noetherian conservation laws for photons

Michael K.-H. Kiessling, A. Shadi Tahvildar-Zadeh( )
Department of Mathematics, Rutgers, The State University of New Jersey (New Brunswick), USA
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Abstract

We review the formulation of a Lorentz-covariant bispinorial wave function and wave equation for a single photon on a flat background. We show the existence of a 10-dimensional set of conservation laws for this equation, and prove that 8 of these can be used to obtain global, gauge-invariant, ADM-like quantities that together define a covariantly constant self-dual bispinor.

Keywords

photon wave functionrelativistic quantum mechanicsDirac's equationgauge-invariant conservation laws
CLC number: 35Q41, 37K06, 70H33, 70S10, 81Q05, 83C40

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Communications in Analysis and Mechanics
Volume 17 Issue 2,
June 2025
Pages 606-629
DOI: 10.3934/cam.2025024

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Cite this article:
Kiessling MK-H, Shadi Tahvildar-Zadeh A. Noetherian conservation laws for photons. Communications in Analysis and Mechanics, 2025, 17(2): 606-629. https://doi.org/10.3934/cam.2025024

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Received: 02 February 2025
Revised: 24 April 2025
Accepted: 06 May 2025
Published: 16 June 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)