Local and asymptotic structure of quantum systems with superselection rules

The authors' algebraic description of an arbitrary quantum system with superselection rules is used to investigate the local and asymptotic structure of such systems. The main attention is devoted to the equivalence properties of coherent superselection sectors. It is shown that physical (weak) equivalence of coherent sectors is not guaranteed by the Haag–Araki postulates and that it is equivalent to the quasilocal algebra's being simple, the condition of extended locality, and the globality property of the superseleetion operators. The structure of the quasilocal algebra ideals is completely described. An “asymptotic” condition is introduced; it guarantees asymptotic unitary equivalence of coherent sectors and also that all vector states are asymptotically close (with respect to space-like translations) to the vacuum state.