Gauge-symmetrization method for energy-momentum tensors in high-order electromagnetic field theories
Abstract
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 $$F_{μν}$$, instead of the 4-potential $$A_{μ}$$, to derive a canonical EMT $$T^{μν}_{N}$$. We show that the gauge-dependent part of $$T^{μν}_{N}$$ can be removed using the displacement-potential tensor $$F^{σμν}$$ ≡ $$D^{σμ}A^{ν}/4π$$, where $$D^{σμ}$$ 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, $$F^{σμν}$$ reduces to the familiar BR superpotential $$S^{σμν}$$, and the method developed can be used as a simpler procedure to calculate $$S^{σμν}$$ 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.
- Authors:
-
[1];
- Shenzhen Univ. (China) College of Physics and Optoelectronic Engineering, Key Laboratory of Optoelectronic Devices and Systems; Shenzhen Univ. (China). Advanced Energy Research Center
- Univ. of Science and Technology of China, Hefei (China). School of Nuclear Science and Technology
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Publication Date:
- Research Org.:
- Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)
- Sponsoring Org.:
- Shenzhen Clean Energy Research Institute; National Natural Science Foundation of China (NSFC)
- OSTI Identifier:
- 1814592
- Grant/Contract Number:
- AC02-09CH11466; NSFC-12005141; NSFC-11905220; 11805273; 2016YFA0400600; 2016YFA0400601; 2016YFA0400602; 2018YFE0304100
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review D
- Additional Journal Information:
- Journal Volume: 104; Journal Issue: 2; Journal ID: ISSN 2470-0010
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; classical field theory; classical mechanics; continuum mechanics; electromagnetism; high-energy-density plasmas; thermal and statistical models
Citation Formats
Fan, Peifeng, Xiao, Jianyuan, and Qin, Hong. Gauge-symmetrization method for energy-momentum tensors in high-order electromagnetic field theories. United States: N. p., 2021.
Web. doi:10.1103/physrevd.104.025013.
Fan, Peifeng, Xiao, Jianyuan, & Qin, Hong. Gauge-symmetrization method for energy-momentum tensors in high-order electromagnetic field theories. United States. https://doi.org/10.1103/physrevd.104.025013
Fan, Peifeng, Xiao, Jianyuan, and Qin, Hong. Fri .
"Gauge-symmetrization method for energy-momentum tensors in high-order electromagnetic field theories". United States. https://doi.org/10.1103/physrevd.104.025013. https://www.osti.gov/servlets/purl/1814592.
@article{osti_1814592,
title = {Gauge-symmetrization method for energy-momentum tensors in high-order electromagnetic field theories},
author = {Fan, Peifeng and Xiao, Jianyuan and Qin, Hong},
abstractNote = {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 $F_{μν}$, instead of the 4-potential $A_{μ}$, to derive a canonical EMT $T^{μν}_{N}$. We show that the gauge-dependent part of $T^{μν}_{N}$ can be removed using the displacement-potential tensor $F^{σμν}$ ≡ $D^{σμ}A^{ν}/4π$, where $D^{σμ}$ 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, $F^{σμν}$ reduces to the familiar BR superpotential $S^{σμν}$, and the method developed can be used as a simpler procedure to calculate $S^{σμν}$ 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.},
doi = {10.1103/physrevd.104.025013},
journal = {Physical Review D},
number = 2,
volume = 104,
place = {United States},
year = {Fri Jul 16 00:00:00 EDT 2021},
month = {Fri Jul 16 00:00:00 EDT 2021}
}
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