Noetherian conservation laws for photons

Michael K.-H. Kiessling; A. Shadi Tahvildar-Zadeh; Michael K.-H. Kiessling; A. Shadi Tahvildar-Zadeh

doi:10.3934/cam.2025024

Communications in Analysis and Mechanics

2025, Volume 17, Issue 2: 606-629. doi: 10.3934/cam.2025024

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Noetherian conservation laws for photons

Department of Mathematics, Rutgers, The State University of New Jersey (New Brunswick), USA

Received: 02 February 2025 Revised: 24 April 2025 Accepted: 06 May 2025 Published: 16 June 2025
35Q41, 37K06, 70H33, 70S10, 81Q05, 83C40

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.
- photon wave function,
- relativistic quantum mechanics,
- Dirac's equation,
- gauge-invariant conservation laws
Citation: Michael K.-H. Kiessling, A. Shadi Tahvildar-Zadeh. Noetherian conservation laws for photons[J]. Communications in Analysis and Mechanics, 2025, 17(2): 606-629. doi: 10.3934/cam.2025024

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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.

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