Quantum particles in noncommutative spacetime: An identity crisis

We argue that the notion of identical particles is no longer well defined in quantum systems governed by non-commutative deformations space-time symmetries. Such models are characterized four-momentum space given a non-abelian Lie group. Our analysis based on observation that, for states containing more than one particle, only total momentum system number. obtained from composition individual momenta which uniquely defined. The main upshot our all previous attempts to construct Fock spaces these rested wrong assumptions and indeed have been unsuccessful. also show how natural braiding numbers characterizes exchange factors tensor product covariant under relativistic transformations thus solving long standing problem field.