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It is shown that only one vacuum state can be prepared with a finite amountof energy and it appears, in particular, as a limit of physical states underlarge timelike translations in any theory which satisfies a phase spacecondition proposed in this work. This new criterion, related to the concept ofadditivity of energy over isolated subsystems, is verified in massive freefield theory. The analysis entails very detailed results about the momentumtransfer of local operators in this model.

A sharpened nuclearity condition and the uniqueness of the vacuum in QFT