An Algebraic Model for Quantum Unstable States

In this review, we present a rigorous construction of an algebraic method for quantum unstable states, also called Gamow states. A traditional picture associates these states to vectors states called Gamow vectors. However, this has some difficulties. In particular, there is no consistent definition of mean values of observables on Gamow vectors. In this work, we present Gamow states as functionals on algebras in a consistent way. We show that Gamow states are not pure states, in spite of their representation as Gamow vectors. We propose a possible way out to the construction of averages of observables on Gamow states. The formalism is intended to be presented with sufficient mathematical rigor.

Automated summary

This review presents a rigorous algebraic method for constructing quantum unstable states, also known as Gamow states. Traditionally, these states are associated with vector states called Gamow vectors, but there are difficulties in doing so. The authors present Gamow states as functionals on algebras in a consistent way and propose a possible method for constructing averages of observables on Gamow states.