TwoTwistor Space, Commuting Composite Minkowski Coordinates and Particle Dynamics.pdfVIP

Two-Twistor Space, Commuting Composite Minkowski Coordinates and Particle Dynamics 5 A. Bette1) , J. Lukierski2) and C. MiquelEspanya3) 0 0 2 1) Royal Institute of Technology r a S151 81 S¨odert¨alje, Sweden M 2)Institute for Theoretical Physics, 6 University of Wroclaw, 1 1 pl. M. Borna 9, 50204 Wroclaw, Poland v 3)Departament de F´ısica Te`orica i IFIC, 4 3 Universitat de Val`encia, 1 3 Dr. Moliner 50, 46100 Burjassot (Val`encia), Spain 0 5 0 / Abstract h t- We employ the modification of the basic Penrose formula in twistor theory, which p allows to introduce commuting composite space-time coordinates. It appears that in e h the course of such modification the internal symmetry SU (2) of two-twistor system is : broken to U (1). We consider the symplectic form on two-twistor space, permitting v i to interpret its 16 real components as a phase-space. After a suitable change of X variables such a two-twistor phase space is split into three mutually commuting r a parts, describing respectively the standard relativistic phase space (8 degrees of freedom), the spin sector (6 degrees of freedom) and the canonical pair angle-charge describing the electric charge sector (2 degrees of freedom). We obtain a geometric framework providing a twistor-inspired 18-dimensional extended relativistic phase space M18. In such a space we propose the action only with first class constraints, describing the relativis