Abstract
A quantum generalization of the Cooper-Fry recipe is proposed. The single-particle spectrum arising from relativistic collisions of particles and nuclei is calculated within the thermal quantum field theory framework. The starting point of consideration is the solution of the initial-value problem of particle emission from a space-like hypersurface. In the following steps, we obtain the single-particle spectrum using the ``smaller'' Green's function associated with the fireball medium. Based on this result, several specific examples of particle emission are considered.