Gamov algebras

We introduce the extended algebra of observables associated with the Rigged Fock Space in order to make a new step towards the description of unstable quantum systems. In particular, we study three exactly solvable models in second quantization representation, namely the standard Friedrichs model, the Friedrichs model with virtual transitions and a relativistic model of two interacting fields and provide a mathematical formalism for their description. This is a first step towards a new generalization of the algebra of observables corresponding to the non-factorizable extensions of Liouville evolution.