  A slight modification of one axiom of quantum theory changes a reversible
theory into a time asymmetric theory. Whereas the standard Hilbert space axiom
does not distinguish mathematically between the space of states (in-states of
scattering theory) and the space of observables (out-``states'' of scattering
theory) the new axiom associates states and observables to two different Hardy
subspaces which are dense in the same Hilbert space and analytic in the lower
and upper complex energy plane, respectively. As a consequence of this new
axiom the dynamical equations (Schr\"{o}dinger or Heisenberg) integrate to a
semigroup evolution. Extending this new Hardy space axiom to a relativistic
theory provides a relativistic theory of resonance scattering and decay with
Born probablilities that fulfill Einstein causality and the exponential decay
law.
