Resonance Phenomena and time asymmetric quantum mechanics

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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