** Authors:**
ARNO RUDOLF BOHM, FATİH ERMAN, HAYDAR UNCU

** Abstract: **
This article is a review of time asymmetric quantum theory
and its consequences applied to the resonance and decay phenomena. We
first give some phenomenological results about resonances and decaying
states to support the popular idea that resonances characterized by a
width \Gamma and decaying states characterized by a lifetime \tau are
different appearances of the same physical entity. Based on
Weisskopf-Wigner (WW) methods, one obtains approximately
\frac{\hbar}{\tau}\approx \Gamma. However, using standard axioms of
quantum physics it is not possible to establish a rigorous theory to
which the 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 Hilbert space
H. Modifying this Hilbert space axiom to a Hardy space axiom one
distinguishes the prepared (in) states and detected (out) observables.
This leads to semi-group time evolution and to beginnings of time for
individual microsystems. As a consequence of this time asymmetric
theory one derives \frac{\hbar}{\tau} = \Gamma as an exact relation,
and this unifies resonances and decaying states. Finally, we show
that this unification can also be extended to the relativistic regime.

** Keywords: **
Time asymmetric quantum theory, resonances, decaying states

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