2021/03/26 by Peifeng Fan, Jianyuan Xiao, Hong Qin
Physics and Astronomy · #Electromagnetic field #Electromagnetic tensor #Gauge anomaly #Gauge theory #Geometry #Introduction to gauge theory #Ionosphere and magnetosphere dynamics #Lagrangian #Magnetic confinement fusion research #Mathematical descriptions of the electromagnetic field #Mathematical physics #Noether's theorem #Order (exchange) #Physics #Quantum mechanics #Solar and Space Plasma Dynamics #Tensor (intrinsic definition) #physics.class-ph
paper · pdf · doi:10.1103/physrevd.104.025013
published as Phys. Rev. D 104, 025013 (2021)
arxiv created 2021/03/26 · openalex publication_date 2021/07/16 · arxiv updated 2021/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
For electromagnetic field theories, canonical energy-momentum conservation laws can be derived from the underpinning spacetime translation symmetry according to the Noether procedure. However, the canonical energy-momentum tensors (EMTs) are neither symmetric nor gauge-symmetric (gauge invariant). The Belinfante-Rosenfeld (BR) method is a well-known procedure to symmetrize the EMTs, which also renders them gauge symmetric for first-order field theories. High-order electromagnetic field theories appear in the study of gyrokinetic systems for magnetized plasmas and the Podolsky system for the radiation reaction of classical charged particles. For these high-order field theories, gauge-symmetric EMTs are not necessarily symmetric and vice versa. In the present study, we develop a new gauge-symmetrization method for EMTs in high-order electromagnetic field theories. The Noether procedure is carried out using the Faraday tensor F_\ensuremathμ\ensuremathν, instead of the 4-potential A_\ensuremathμ, to derive a canonical EMT TN^\ensuremathμ\ensuremathν. We show that the gauge-dependent part of TN^\ensuremathμ\ensuremathν can be removed using the displacement-potential tensor F^\ensuremathσ\ensuremathμ\ensuremathν\ensuremath≡D^\ensuremathσ\ensuremathμA^\ensuremathν/4\ensuremathπ, where D^\ensuremathσ\ensuremathμ is the antisymmetric electric displacement tensor. This method gauge-symmetrizes the EMT without necessarily making it symmetric, which is adequate for applications not involving general relativity. For first-order electromagnetic field theories, such as the standard Maxwell system, F^\ensuremathσ\ensuremathμ\ensuremathν reduces to the familiar BR superpotential S^\ensuremathσ\ensuremathμ\ensuremathν, and the method developed can be used as a simpler procedure to calculate S^\ensuremathσ\ensuremathμ\ensuremathν without employing the angular momentum tensor in 4D spacetime. When the electromagnetic system is coupled to classical charged particles, the gauge-symmetrization method for EMTs is shown to be effective as well.