Test Particles with Acceleration-Dependent Lagrangian

Details Test Particles with Acceleration-Dependent Lagrangian Test Particles with Acceleration-Dependent Lagrangian

2005-10-04

arxiv.org/abs/hep-th/0510030v2

J.Math.Phys. 47 (2006) 022904

Physics

High Energy Physics

High Energy Physics - Theory

36 pages, no figures, LATEX, some new comments and new references added

Scientific paper

10.1063/1.2170486

We consider a classical test particle subject to electromagnetic and gravitational fields, described by a Lagrangian depending on the acceleration and on a fundamental length. We associate to the particle a moving local reference frame and we study its trajectory in the principal fibre bundle of all the Lorentz frames. We discuss in this framework the general form of the Lagrange equations and the connection between symmetries and conservation laws (Noether theorem). We apply these results to a model, already discussed by other authors, which implies an upper bound to the proper acceleration and to another new model in which a similar quantity, called ``pseudo-acceleration'', is bounded. With some simple choices of the fields, we illustrate some other interesting properties of the models and we show that unwanted features may appear, as unstable run-away solutions and unphysical values of the energy-momentum or of the velocity.

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