XXV Workshop on Geometric Methods in Physics 2-8.07.2006

Haydar Uncu

Unification of Resonances and Decaying States with Time Asymmetric Quantum Theory

In this study, we briefly review some established results in time asymmetric quantum theory for resonances and decaying states. The resonances and decaying states are considered to be different appearances of the same physical entity based on Wigner-Weisskopf (WW) approximation. However, using standard axioms of quantum physics it is not possible to establish a rigorous theory in which various WW methods can be considered as approximations. In standard quantum theory, the set of states and the set of observables are mathematically identified and described by the same linear vector space H (Hilbert space axiom). Modifying this axiom to Hardy space axiom one distinguishes the prepared (in) states and detected (out) observables. This leads to semi-group time evolution and beginnings of time for individual microsystems. As a consequence of this time asymmetric theory one naturally obtaines $\hbar/\tau=\Gamma$ as an exact relation and therefore unify resonances and decaying states.