Communications in Mathematical Physics

, Volume 35, Issue 1, pp 49-85

First online:

Local observables and particle statistics II

  • Sergio DoplicherAffiliated withIstituto Nazionale di Fisica Nucleare and Istituto Matematico G. Castelnuovo, Università di Roma
  • , Rudolf HaagAffiliated withII. Institut für Theoretische Physik der Universität
  • , John E. RobertsAffiliated withII. Institut für Theoretische Physik der Universität

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Starting from the principles of local relativistic Quantum Theory without long range forces, we study the structure of the set of superselection sectors (charge quantum numbers) and its implications for the particle aspects of the theory. Without assuming the commutation properties (or even the existence) of unobservable fields connecting different sectors (charge-carrying fields), one has a particle-antiparticle symmetry, an intrinsic notion of statistics for identical particles, and a spin-statistics theorem. Particles in “pseudoreal sectors” cannot be their own antiparticles (a variant of Carruthers' theorem). We also show how scattering states and transition probabilities are obtained in this frame.