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Peifeng FAN, Qiang CHEN, Jianyuan XIAO, Zhi YU. High-order field theory and a weak Euler–Lagrange–Barut equation for classical relativistic particle-field systems[J]. Plasma Science and Technology, 2023, 25(11): 115001. DOI: 10.1088/2058-6272/acdc07
Citation: Peifeng FAN, Qiang CHEN, Jianyuan XIAO, Zhi YU. High-order field theory and a weak Euler–Lagrange–Barut equation for classical relativistic particle-field systems[J]. Plasma Science and Technology, 2023, 25(11): 115001. DOI: 10.1088/2058-6272/acdc07

High-order field theory and a weak Euler–Lagrange–Barut equation for classical relativistic particle-field systems

More Information
  • Corresponding author:

    Peifeng FAN, E-mail: pffan@ahu.edu.cn

  • Received Date: January 02, 2023
  • Revised Date: April 19, 2023
  • Accepted Date: June 05, 2023
  • Available Online: December 05, 2023
  • Published Date: July 12, 2023
  • In both quantum and classical field systems, conservation laws such as the conservation of energy and momentum are widely regarded as fundamental properties. A broadly accepted approach to deriving conservation laws is built using Noether's method. However, this procedure is still unclear for relativistic particle-field systems where particles are regarded as classical world lines. In the present study, we establish a general manifestly covariant or geometric field theory for classical relativistic particle-field systems. In contrast to quantum systems, where particles are viewed as quantum fields, classical relativistic particle-field systems present specific challenges. These challenges arise from two sides. The first comes from the mass-shell constraint. To deal with the mass-shell constraint, the Euler–Lagrange–Barut (ELB) equation is used to determine the particle's world lines in the four-dimensional (4D) Minkowski space. Besides, the infinitesimal criterion, which is a differential equation in formal field theory, is reconstructed by an integro-differential form. The other difficulty is that fields and particles depend on heterogeneous manifolds. To overcome this challenge, we propose using a weak version of the ELB equation that allows us to connect local conservation laws and continuous symmetries in classical relativistic particle-field systems. By applying a weak ELB equation to classical relativistic particle-field systems, we can systematically derive local conservation laws by examining the underlying symmetries of the system. Our proposed approach provides a new perspective on understanding conservation laws in classical relativistic particle-field systems.

  • PF was supported by National Natural Science Foundation of China (No. 12005141). QC was supported by National Natural Science Foundation of China (No. 11805273). JX was supported by the Collaborative Innovation Program of Hefei Science Center, CAS (No. 2021HSCCIP019), National MC Energy R&D Program (No. 2018YFE0304100), and National Natural Science Foundation of China (No. 11905220).

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