Canonical Dynamics of Spinning Particles in Gravitational and Electromagnetic Fields

In terms of the canonical form and the connection form on the bundle of Lorentz frames P over a space-time manifold V, a presymplectic form ω is defined on P, which induces a Poisson bracket on the set of real valued functions on the phase space of the system representing a spinning particle in an exterior gravitational and electromagnetic field. This structure coincides with the unique Poincaré invariant one for the free particle. Moreover, the projections into V of the integral manifolds of the kernel of ω on P yield precisely the world lines of a spinning particle as obtained for the dipole approximation of Dixon's equations of motion for extended test bodies in general relativity.