DOI number: 10.1007/s11467-018-0793-z

Journal: Frontiers of Physics

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

Abstract: 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.

Co-author: Peifeng Fan,Hong Qin,Jian Liu,Nong Xiang,Zhi Yu

Discipline: Natural Science

Volume: 13

Issue: 4

Page Number: 135203

Translation or Not: no

Date of Publication: 2018-08-07

Included Journals: SCI

Links to published journals: https://journal.hep.com.cn/fop/EN/10.1007/s11467-018-0793-z