CONFORMAL SYMMETRY AND QUANTUM RELATIVITY

The relativistic conception of space and time is challenged by the qua ntum nature of physical observables. Ir has been known for a long time that Poincare symmetry of field theory can be extended to the larger conformal symmetry. We use these symmetries to define quantum observab les associated with positions in space-time, in the spirit of Einstein theory of relativity. This conception of localization may be applied to massive as well as massless fields. Localization observables are de fined as to obey Lorentz covariant commutation relations and in partic ular include a time observable conjugated to energy. While position co mponents do not commute in the presence of a nonvanishing spin, they s till satisfy quantum relations which generalize the differential laws of classical relativity. We also give of these observables a represent ation in terms of canonical spatial positions, canonical spin componen ts, and a propel time operator conjugated to mass. These results plead for a new representation not only of space-time localization but also of motion.