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

作　　者：范培锋 陈强 肖建元 于治 Peifeng FAN;Qiang CHEN;Jianyuan XIAO;Zhi YU(School of Physics and Optoelectronic Engineering,Anhui University,Hefei 230601,People’s Republic of China;National Supercomputing Center in Zhengzhou,Zhengzhou University,Zhengzhou 450001,People’s Republic of China;School of Nuclear Science and Technology,University of Science and Technology of China,Hefei 230026,People’s Republic of China;Institute of Plasma Physics,Chinese Academy of Sciences,Hefei 230031,People’s Republic of China)

机构地区：[1]School of Physics and Optoelectronic Engineering,Anhui University,Hefei 230601,People’s Republic of China [2]National Supercomputing Center in Zhengzhou,Zhengzhou University,Zhengzhou 450001,People’s Republic of China [3]School of Nuclear Science and Technology,University of Science and Technology of China,Hefei 230026,People’s Republic of China [4]Institute of Plasma Physics,Chinese Academy of Sciences,Hefei 230031,People’s Republic of China

出　　处：《Plasma Science and Technology》2023年第11期42-54,共13页等离子体科学和技术（英文版）

基　　金：supported by National Natural Science Foundation of China(No.12005141);supported by National Natural Science Foundation of China(No.11805273);supported by the Collaborative Innovation Program of Hefei Science Center,CAS(No.2021HSCCIP019);National MC Energy R&D Program(No.2018YFE0304100);National Natural Science Foundation of China(No.11905220)。

摘　　要：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.

关 键 词：high-order field theory weak Euler-Lagrange-Barut equation infinitesimal criterion of symmetric condition Noether's theorem geometric conservation laws 

分 类 号：O412.1[理学—理论物理]