Complete Integrability for Lagrangian Dependent on Acceleration in a Space-Time of Constant Curvature

Details Complete Integrability for Lagrangian Dependent on Acceleration in a Space-Time of Constant Curvature Complete Integrability for Lagrangian Dependent on Acceleration in a Space-Time of Constant Curvature

1995-05-11

arxiv.org/abs/hep-th/9505064v1

Class.Quant.Grav. 13 (1996) 1201-1212

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, LATEX

Scientific paper

10.1088/0264-9381/13/5/030

The equations of motion for a Lagrangian ${\cal L}(k_1)$, depending on the curvature $k_1$ of the particle worldline, embedded in a space--time of constant curvature, are considered and reformulated in terms of the principal curvatures. It is shown that for arbitrary Lagrangian function ${\cal L}(k_1)$ the general solution of the motion equations can be obtained by integrals. By analogy with the flat space--time case, the constants of integration are interpreted as the particle mass and its spin. As examples, we completely investigate Lagrangians linear and quadratic in $(k_1)$ and the model of relativistic particle with maximal proper acceleration, in a space--time with constant curvature.

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