Special bracket versus Jacobi bracket on the classical phase space of general relativistic test particle

Abstract

The classical phase space of general relativistic classical test particle (here called, for short, "phase space") is defined as the first jet space of motions regarded as timelike one-dimensional submanifolds of spacetime. By the projectability assumption, we define the subsheaf of special phase functions with a special Lie bracket and we compare the Lie algebra of special phase functions with the structures obtained on the phase space by the standard Hamiltonian approach.