EXTENDED PHASE SPACES AND TWISTER THEORY

A commuting Minkowski position variable in the two-twister phase space is found, providing a link between twister phase spaces and the exten ded phase spaces for an elementary spinning particle, as defined by Za krzewski. The two-twister phase space is shown to be the product of th ree symplectic manifolds: the (forward) cotangent bundle to the Minkow ski spacetime, the cotangent bundle to a circle (electric charge phase space) and the cotangent bundle to the real projective spinor space. The decomposition of the latter into Lorentz-'irreducible' parts gives exactly the one-parameter family of extended phase spaces described b y Zakrzewski for b = 0 (and arbitrary a).