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A new phase space criterion, encoding the physically motivated behavior ofcoincidence arrangements of local observables, is proposed in this work. Thiscondition entails, in particular, uniqueness and purity of the energeticallyaccessible vacuum states. It is shown that the qualitative part of this newcriterion is equivalent to a compactness condition proposed in the literature.Its novel quantitative part is verified in massive free field theory.

Coincidence Arrangements of Local Observables and Uniqueness of the Vacuum in QFT