Relativistic particles and the geometry of 4-D null curves |
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Authors: | Angel Ferrández Angel Giménez Pascual Lucas |
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Institution: | 1. Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Murcia, Spain;2. Centro de Investigación Operativa, Universidad Miguel Hernández, Avda. Universidad s/n, 03202 Elche, Alicante, Spain |
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Abstract: | 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. |
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Keywords: | 04 20 -q 02 40 -k |
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