On the Localizability of Massless Particles

Abstract

Wightman's reformulation of the Wigner-Newton position operators and localizability of a massive particle is generalized so as to include zero mass particles. Different a priori procedures of generalizations are examined: we first prove some negative results based upon a projective induction technique. We then present some positive results which state that in some sense zero-mass particles are localizable and that their corresponding position operators are candidates for observables. Our treatment–which is group theoretical and kinematical in the same sense as that of Wightman–ends with suggestions for further possible developments.