Abstract

The discussion on the correspondence between unstable particles and poles of the $S$ matrix, started in a previous paper, is continued with particular attention to the decay law. It is shown that the previous formalism can be modified to obtain an $S$ matrix, satisfying all the usual requirements of analyticity, unitarity, and asymptotic behavior, which exhibits an isolated resonance with exponential decay without an accompanying pole in the unphysical sheet. The existence of a local potential which yields the $S$ matrix considered is also proved.

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