Gauge-symmetrization method for energy-momentum tensors in high-order electromagnetic field theories

Journal Article · Fri Jul 16 00:00:00 EDT 2021 · Physical Review D

DOI:https://doi.org/10.1103/physrevd.104.025013· OSTI ID:1814592

Fan, Peifeng ^[1]; Xiao, Jianyuan ^[2]; Qin, Hong ^[3]

---

1. Shenzhen Univ. (China) College of Physics and Optoelectronic Engineering, Key Laboratory of Optoelectronic Devices and Systems; Shenzhen Univ. (China). Advanced Energy Research Center
2. Univ. of Science and Technology of China, Hefei (China). School of Nuclear Science and Technology
3. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)

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.

• Research Organization: Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)
• Sponsoring Organization: National Natural Science Foundation of China; Shenzhen Clean Energy Research Institute
• Grant/Contract Number: AC02-09CH11466
• OSTI ID: 1814592
• Journal Information: Physical Review D, Journal Name: Physical Review D Journal Issue: 2 Vol. 104; ISSN 2470-0010
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
classical field theory
classical mechanics
continuum mechanics
electromagnetism
high-energy-density plasmas
thermal and statistical models