Dirac's causality leads to time asymmetry

On the basis of Dirac's causality, we will show that the time evolution is limited to a semigroup. The abstract vector space for states and (yes-or-no) observables are then not the entire Hilbert space but its particular dense subspaces, called Hardy spaces. The Hardy spaces and their functional spaces together make the Hardy rigged Hilbert spaces, which is also called the time-asymmetric boundary condition (TABC). We will illustrate the usage of the TABC with the neutral kaon decay experiment.