0 v 1 1 2 D ec 1 99 4 Extended phase space for a spinning particle

Extended phase space of an elementary (relativistic) system is introduced in the spirit of the Souriau’s definition of the ‘space of motions’ for such system. Our ‘modification’ consists in taking into account not only the symmetry (Poincaré) group but also its action on the (Minkowski) space-time, i.e. the full covariant system. This yields a general procedure to construct spaces in which the equations of motion can be formulated: phase trajectories of the system are identified as characteristics on some constraint submanifold (‘mass and spin shell’) in the extended phase space. Our formulation is generally applicable to any homogeneous space-time (e.g. de Sitter) and also to Poisson actions. Calculations concerning the Minkowski case for non-zero spin particles show an intriguing alternative: we should either accept two-dimensional trajectories or (Poisson) noncommuting space-time coordinates.