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

References in corpus (5)

• Jacobi structures revisited
• From Green Function to Quantum Field
• Equations of Motion as Constraints: Superselection Rules, Ward Identities
• Differential Calculus on Manifolds with a Boundary. Applications
• Time, classical and quantum

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• Covariant Variational Evolution and Jacobi Brackets: Particles
• Covariant reduction of classical Hamiltonian Field Theories: From D'Alembert to Klein-Gordon and Schrödinger
• Topological and dynamical aspects of Jacobi sigma models