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The analytic continuation of the Lippmann-Schwinger bras and kets is obtainedand characterized. It is shown that the natural mathematical setting for theanalytic continuation of the solutions of the Lippmann-Schwinger equation isthe rigged Hilbert space rather than just the Hilbert space. It is also arguedthat this analytic continuation entails the imposition of a time asymmetricboundary condition upon the group time evolution, resulting into a semigrouptime evolution. Physically, the semigroup time evolution is simply a (retardedor advanced) propagator.Comment: 32 pages, 3 figure

The rigged Hilbert space approach to the Lippmann–Schwinger equation: II. The analytic continuation of the Lippmann–Schwinger bras and kets