Indefinite metric and asymptotic probabilities

Summary

The probability interpretation of quantum structures is determined by the time representations involved. Finite-dimensional faithful representations of the noncompact realsR as time model lead to an indefinite metric. Also those nonunitary time representations with nilpotent partse.g., arising in the free motion in Newtons mechanics, allow an asymptotic state space with well-defined probabilities. Compared with the unitary Feynman propagators, connected with the Fock state, the time-space propagators of noncompact time representations display a different analytical structure.