Coherent states for $Sp(2,2)$ and geometrized decay model for an unstable system

The decay amplitude of an unstable particle in a relativistic geometrized model is calculated. The states of the unstable system at an arbitrary instant of time are constructed as coherent states on the discrete series of unitary irreducible representations of the group $Sp(2,2)$ and are parametrized by a point of the hyperboloid $\xi^2=-\rho^2$. The radius of curvature $\rho$ is related to the coupling constant and the energy. The transition to the limit of stable objects is investigated.