A superselection rule partitions a representation into sectors between which the specified observable algebra has no matrix elements. Relative phases between vectors in different sectors cannot be detected by those observables, so a coherent vector spanning sectors and its sector-diagonal mixture define the same observable state. The restriction is relative to the observable algebra; it is not by itself a physical wave-function collapse. Infinite-system phases can yield disjoint representations and emergent superselection sectors even though each finite system permits global connecting operators.
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