EXTENDED PHASE-SPACE FOR A SPINNING PARTICLE

The extended phase space of an elementary (relativistic) system is int roduced in the spirit of Souriau's definition of the 'space of motions ' for such a system. Our 'modification' consists in taking into accoun t not only the symmetry (Poincare) group but also its action on the (M inkowski) spacetime, i.e. the full covariant system. This yields a gen eral procedure to construct spaces in which the equations of motion ca n be formulated: phase trajectories of the system are identified as ch aracteristics on some constraint submanifold ('mass and spin shell') i n the extended phase space. Our formulation is generally applicable to any homogeneous spacetime (e.g, de Sitter) and also to Poisson action s. Calculations concerning the Minkowski case for non-zero spin partic les show an intriguing alternative: we should either accept two-dimens ional trajectories or (Poisson) non-commuting spacetime coordinates.