Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-05-03
Class.Quant.Grav. 18 (2001) 5065-5084
Physics
High Energy Physics
High Energy Physics - Theory
20 pages, no figures - replaced with version to appear in Class. Quant. Grav. - minor changes, added Conclusions section
Scientific paper
10.1088/0264-9381/18/23/304
We consider the motion of a particle described by an action that is a functional of the Frenet-Serret [FS] curvatures associated with the embedding of its worldline in Minkowski space. We develop a theory of deformations tailored to the FS frame. Both the Euler-Lagrange equations and the physical invariants of the motion associated with the Poincar\'e symmetry of Minkowski space, the mass and the spin of the particle, are expressed in a simple way in terms of these curvatures. The simplest non-trivial model of this form, with the lagrangian depending on the first FS (or geodesic) curvature, is integrable. We show how this integrability can be deduced from the Poincar\'e invariants of the motion. We go on to explore the structure of these invariants in higher-order models. In particular, the integrability of the model described by a lagrangian that is a function of the second FS curvature (or torsion) is established in a three dimensional ambient spacetime.
Arreaga Guillermo
Capovilla Riccardo
Guven Jemal
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