Relativistic particles and the geometry of 4-D null curves

被引:20
作者
Fernandez, Angel
Gimenez, Angel
Lucas, Pascual
机构
[1] Univ Murcia, Dept Matemat, E-30100 Murcia, Spain
[2] Univ Miguel Hernandez, Ctr Invest Operativa, Alicante 03202, Spain
关键词
Lagrangian; Euler-Lagrange equations; null curve; critical point; killing field; Henon-Heiles systems;
D O I
10.1016/j.geomphys.2007.05.006
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We study actions in (d + 1)-dimensions associated with null curves, mainly when d = 3, whose Lagrangian is a linear function on the curvature of the particle path, showing that null helices are always possible trajectories of the particles. We find Killing vector fields along critical curves of the action which correspond to the linear and the angular momenta of the particle. They provide two constants of the motion which can be interpreted in terms of the mass and the spin of the system. Moreover, we are able to integrate both the Euler-Lagrange equations and the Cartan equations in cylindrical coordinates around a certain plane. (c) 2007 Elsevier B.V. All rights reserved.
引用
收藏
页码:2124 / 2135
页数:12
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