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DOI码：10.1007/s11467-018-0793-z

发表刊物：Frontiers of Physics

关键字：relativistic particle-field system / different manifolds / mass-shell constraint / geometric weak Euler–Lagrange equation / symmetry / conservation laws

摘要：A manifestly covariant, or geometric, field theory of relativistic classical particle-field systems is developed. The connection between the space-time symmetry and energy-momentum conservation laws of the system is established geometrically without splitting the space and time coordinates; i.e., spacetime is treated as one entity without choosing a coordinate system. To achieve this goal, we need to overcome two difficulties. The first difficulty arises from the fact that the particles and the field reside on different manifolds. As a result, the geometric Lagrangian density of the system is a function of the 4-potential of the electromagnetic fields and also a functional of the particles’ world lines. The other difficulty associated with the geometric setting results from the mass-shell constraint. The standard Euler–Lagrange (EL) equation for a particle is generalized into the geometric EL equation when the mass-shell constraint is imposed. For the particle-field system, the geometric EL equation is further generalized into a weak geometric EL equation for particles. With the EL equation for the field and the geometric weak EL equation for particles, the symmetries and conservation laws can be established geometrically. A geometric expression for the particle energy-momentum tensor is derived for the first time, which recovers the non-geometric form in the literature for a chosen coordinate system.

合写作者：Peifeng Fan,Hong Qin,Jian Liu,Nong Xiang,Zhi Yu

学科门类：理学

卷号：13

期号：4

页面范围：135203

是否译文：否

发表时间：2018-08-07

收录刊物：SCI

发布期刊链接：https://journal.hep.com.cn/fop/EN/10.1007/s11467-018-0793-z