Covariant Jacobi Brackets for Test Particles

Abstract

We show that the space of observables of test particles carries a natural Jacobi structure which is manifestly invariant under the action of the Poincaré group. Poisson algebras may be obtained by imposing further requirements. A generalization of Peierls procedure is used to extend this Jacobi bracket on the space of time-like geodesics on Minkowski space-time.

13 pages Submitted to MPLA